ROOTS OF QUADRATIC EQUATION WORKSHEET

Question 1 :

Find the sum and the product of the roots of the following equations.

(i) x²-6x+5  =  0         Solution

(ii) kx²+rx+pk  =  0        Solution

(iii) 3x²-5x  =  0         Solution

(iv) 8x²-25  =  0         Solution

Question 2 :

Form a quadratic equation whose roots are

(i)  3, 4        Solution

(ii) 3+√7, 3-√7           Solution

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

Question 3 :

If α and β are the roots of the equation

3x²-5x+2  =  0

then find the values of

(i) (α/β) + (β/α)

(ii) α - β

(iii) (α²/β) + (β²/α)        Solution

Question 4 :

If α and β are the roots of

3x²-6x+4  =  0

find the value of α²+β²                    Solution

Question 5 :

If roots of the equation x² + x + r = 0 are α and β and α³+β³ = -6. Find the value of r.

Solution

Question 6 :

If difference between the roots of the equation x² - kx + 8 = 0 is 4, then find the value of k.

Solution

Question 5 :

If one of the roots of the equation

x² + px + a = 0 is √3+2

then find the value of p and a is.

Solution

Question 6 :

If one root of the equation 

px² + qx + r = 0 

is r then other roots of the equation will be

a)  1/q      b)  1/r      c)  1/p      d) 1/(p + q)

Solution

Question 7 :

One root of the equation 

x² - 2(5 + m) x + 3(7 + m) = 0

is reciprocal of the other. Find the value of m.

a)  -7      b)  7      c)  1/7      d) -1/7

Solution

Question 8 :

If α and β are the roots of

2x²-3x-5  =  0

form a quadratic equation whose roots are α² and β²

Solution

Question 9 :

If α and β are the roots of

x²-3x+2  =  0

form a  quadratic equation whose roots are -α and -β.

Solution

Question 10 :

If α and β are the roots of

x²-3x-1  =  0

then form a quadratic equation whose roots are 1/α² and 1/β².            Solution

Question 11 :

If α and β are the roots of the equation

3x²-6x+1  =  0

form an equation whose roots are

(i) 1/α , 1/β   (ii) α²β , β²α   (iii) 2α+β, 2β+α

Solution

Question 12 :

Given that α + β = 5 and α β = -2, find the values of 

a)  (α / β) + (β / α)

b)  α³ + β³

c)  1/ α² + (1/ β²)

Solution

Question 13 :

Given that α + β = 5 and α β = 2/3, find the value of 

(α - β)²

Solution

Question 14:

Given that α + β = -3 and α β = 9, find the value of 

i)  α³β + β³α

ii) α / β  + β / α

Solution

Question 15 :

If one root of the equation

2x²-ax+64  =  0

is twice the other, then find the value of a.

Solution

Question 16 :

If α and β are the roots of

5x²-px+1  =  0

and α - β = 1, then find p.               Solution

Question 17 :

If one root of the equation

3x²+kx-81  =  0

is the square of the other, find k.             Solution

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