Question

If 2 is a root of the quadratic equation3x2+px-8=0 and the quadratic equation 4x2-2px+k=0 has equal roots,find the value of k

Answer 1

Here is your answer... Hope it's helpful

Answer 2

SOLUTION :  

Given : 2 is the root of quadratic equation 3x² + px - 8 = 0………….(1)

& 4x² - 2px + k = 0 has equal roots  ………….(2)

On putting the value of given root i.e x = 2 in eq 1 .

3x² + px - 8 = 0

3(2)² + p(2) − 8 = 0

3 × 4 + 2p - 8 = 0

12 + 2p − 8 = 0

4 + 2p = 0

2p = - 4

p = - 4/ 2  = -2

p = - 2

Hence the value of p is - 2.

On putting the value of p = - 2 in eq 2,  

4x² - 2px + k = 0

4x² - 2(- 2)x + k = 0

4x² + 4x + k = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = 4, b =  4 , and c = k

D(discriminant) = b² – 4ac

Given : Quadratic equation has equal roots i.e D = 0  

b² – 4ac = 0

4² – 4(4)(k) = 0

16 – 16k = 0

16 = 16k

k = 16/16  = 1

k = 1

Hence, the value of k  is 1 .

★★ NATURE OF THE ROOTS

If D = 0 roots are real and equal  

If D > 0 roots are real and distinct

If D < 0  No real roots  

HOPE THIS ANSWER WILL HELP YOU…