## Relations Between Roots Worksheet1

The page relations between roots worksheet1 is containing some practice questions.

(1) Find the sum and the product of the roots of the following equations.

(i) x² - 6 x + 5 = 0

(ii) k x² + r x + p k = 0

(iii) 3x² - 5x = 0

(iv) 8 x² - 25 = 0               Solution

(2) Form a quadratic equation whose roots are

(i)  3 , 4

(ii) 3 + √7 , 3 - √7

(iii) (4 + √7)/2 , (4 - √7)/2                  Solution

(3) If α and β are the roots of the equation 3 x² - 5 x + 2 =0 then find the values of

(i) (α/β) + (β/α)

(ii) α - β

(iii) (α²/β) + (β²/α)       Solution

(4) If α and β are the roots of 3 x² - 6 x + 4 = 0, find the value of α² + β² Solution

(5) If α and β are the roots of 2 x² - 3 x - 5 = 0, form a quadratic equation whose roots are α² and β².      Solution

(6) If α and β are the roots of x² - 3 x + 2 = 0, form a  quadratic equation whose roots are -α and -β.       Solution

(7) If α and β are the roots of x² - 3 x - 1 = 0, then form a quadratic equation whose roots are 1/α² and 1/β².    Solution

(8) If α and β are the roots of the equation 3 x² - 6 x + 1 =0,form an equation whose roots are

(i) 1/α , 1/β     Solution

(ii) α² β , β² α    Solution

(iii) 2 α  + β , 2 β + α   Solution

(9) Find a quadratic equation whose roots are the reciprocal of the roots of the equation 4 x² - 3 x - 1 =0.    Solution

(10) If one root of the equation 3 x² + k x - 81 =0 is the square of the other, find k.     Solution

(11) If one root of the equation 2 x² - a x + 64 = 0 is twice the other, then find the value of "a"    Solution

(12) If α and β are the roots of 5 x² - p x + 1 = 0 and α - β = 1, then find p.   Solution relations between roots worksheet1 relations between roots worksheet1 