Question

If one root of x² - 6x + p is twice of other then , find the value of. p

Answer 1

HELLO DEAR,


let the one of its zeros is x
then another is 2x

we know that,

sum of zeros = -b/a

=> x + 2x = -(-6)/1

=> 3x = 6

=> x = 2

NOW,

product of zeros = c/a

=> x × 2x = p/1

=> 2× 2×2 = p

=> p = 8

Answer 2

Given equation is x^2 - 6x + p.

It is in the form of ax^2 + bx + c=0.

Where a =  1, b = -6, c = p.

Let one root be x and another root will be 2x.

We know that product of the roots x * 2x = p/a

                                                           x * 2x = p/1

                                                           2x^2 = p.    ------- (1)



We know that sum of roots x + 2x = -b/a

                                               x + 2x = -6/1

                                               x + 2x = 6

                                               x + 2x - 6 = 0

                                               x = 2.     ------- (2)



Substitute x = 2 in (1), we get

2(2)^2 = p

p = 8.


Therefore the value of p = 8.



Verification:

Substitute the values in the  Quadratic equation, 

x^2 - 6x + p = 0

(2)^2 - 6(2) + 8 = 0

4 - 12 + 8 = 0

-8 + 8 = 0

0 = 0




Hope this helps!