Success in SPM – Additional Mathematics – Form 4 Chapter 2: Quadratic Equations 1. Given i. ii. iii. and + + + are the roots of 3 − 2 + 1 = 0, find ...
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THIS SHEET IS OF ALL THE FORMULAS YOU WILL NEED FOR THE IGCSE ADDITIONAL MATH EXAMINATION. It includes all the formulas you need to memorize for great results and also the ones which will be availa...
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Success in SPM – Additional Mathematics – Form 4
Chapter 2: Quadratic Equations 1. Given and are the roots of 3 − 2 + 1 = 0, find i. + ii. iii.
+
+
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Success in SPM – Additional Mathematics – Form 4
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Success in SPM – Additional Mathematics – Form 4 2. The equation 4 − 8 + 9 = 0 has roots and , find i. + 3 and + 3 ii. and iii.
and
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Success in SPM – Additional Mathematics – Form 4
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Success in SPM – Additional Mathematics – Form 4 3. Given + + = 0 has one root 4 times of another root, find in terms of and .
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Success in SPM – Additional Mathematics – Form 4 4. + 1 − 3 − 4 + 2 + 9 = 0 has a root negative of another root, find .
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Success in SPM – Additional Mathematics – Form 4 5. Given one root of 2 + 5 + 3 − + 5 = 0 is the reciprocal of another root, find .
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Success in SPM – Additional Mathematics – Form 4 6. The roots of the equation 2 + + 3 = 0 where > 0 are and whilst those of the equation 3 − 2 + 3 are
and . Find .
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Success in SPM – Additional Mathematics – Form 4 7. Given + − 5 − = 0 has roots which differ by 4. Find i. The value of each root ii. The value of .
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Success in SPM – Additional Mathematics – Form 4 8. Given that is the root of each of the equations − 5 + = 0 and − 6 + 3 = 0, where ≠ 0, find and .
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Success in SPM – Additional Mathematics – Form 4 9. Given that and are the roots of the equation = − 2, i. Find the value of +
ii.
Prove that = 2 − 3
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Success in SPM – Additional Mathematics – Form 4
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Success in SPM – Additional Mathematics – Form 4 10. Form the quadratic equation for which the sum of the roots is 2 and the sum of the squares of the roots is 18.
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Success in SPM – Additional Mathematics – Form 4 11. Given the equation 3 + − 8 + 4 + 3 + 4 = 0, find the value of for which i. One root is the negative of the other ii. One root is the reciprocal of the other
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Success in SPM – Additional Mathematics – Form 4
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Success in SPM – Additional Mathematics – Form 4 12. Write + 6 + 144 in the form + + and thus obtain expressions for and in terms of . Hence find the range of values of such that + 6 + 144 is positive for all values of , and deduce the corresponding range of values of .
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Success in SPM – Additional Mathematics – Form 4
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Success in SPM – Additional Mathematics – Form 4 13. The equation 3 + + 120 = 0, where > 0, has roots and where − = 3. Evaluate and and hence, or otherwise, find the value of .
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Success in SPM – Additional Mathematics – Form 4 14. Obtain the quadratic equation whose roots are the squares of the roots of the equation 3 − 2 + 5 = 0.
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Success in SPM – Additional Mathematics – Form 4 15. Given that the equation 2 − 2 + 3 = 0 has the roots and , find the equation whose roots are and .
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Success in SPM – Additional Mathematics – Form 4 16. Given that and are the roots of the equation 2 = 3 − 4, i. Form an equation whose roots are − and − . ii. Show that 4 = − 12
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Success in SPM – Additional Mathematics – Form 4
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Success in SPM – Additional Mathematics – Form 4 17. The quadratic equation + + = 0 has roots −2 and 6. Find i. The value of and ii. The range of values of for which the equation + + = has no real roots
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Success in SPM – Additional Mathematics – Form 4 18. The equation − 2 + 3 = 0 has roots and and the equation − 4 + = 0 has
roots and
. Find the value of and of .
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Success in SPM – Additional Mathematics – Form 4 19. Find the values of for which the line = 2 + is a tangent to the curve =
.
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Success in SPM – Additional Mathematics – Form 4 20. Given that 1 and 2 are the roots of + + = 0, state in terms of some or all of , and , i. The condition that 1= 2 ii. The value of 1+ 2
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Success in SPM – Additional Mathematics – Form 4 21. Find the values of for which the line = is a tangent to the curve = 3 − 1.
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Success in SPM – Additional Mathematics – Form 4 22. The line = 2 mees the curve 3 = − 10 at the points A1, 1 and B 2 , 2 i. Obtain the quadratic equation whose roots are 1 and 2 ii. Without solving this equation, find the co-ordinate of the midpoint of AB
