Question

if 2 root is the root of the equation 2x²+bx+12=0 and the equation x²+bx+q=0 has equal roots then q=
(a) 8
(b) 25
(c) -8
(d) -25​

Answer 1

Step-by-step explanation:

the value of q is equal to 25

Answer 2

Given :-

• 2 is the root of the quadratic equation

2x^2+bx + 12 =0

• x^2 + bx + q = 0 his equal roots

Solution :-

2 is the root of the quadratic equation

2x^2 + bx + 12 = 0

Therefore,

2( 2 )^2 + b( 2 ) + 12 = 0

8 + 2b + 12 = 0

2b + 20 = 0

2b = -20

b = -10

Hence, The value of b= -10

Now,

Subsitute the value of b in quadratic equation x^2 + bx + q

Therefore ,

x^2 + ( -10 )x + q = 0

x^2 -10x + q = 0

Now, Comparing this equation with

ax^2 + bx + c = 0

Here, a = 1 , b = -10 , c = q

As we know that ,

x^2 + -10x + q has equal roots

[ b^2 - 4ac determines whether the quadratic equation ax^2 + bx + c = 0 has real roots or not is called the discriminant of the quadratic equation ]

[ So a quadratic equation has

• Two distinct real roots = If b^2 - 4ac > 0

• Two equal real roots = If b^2 - 4ac = 0

• No real roots = if b^2 - 4ac < 0 ]

Therefore,

By using discriminant b^2 - 4ac

Here , a= 1 , b = -10 , c = q

Put the required values in discriminant,

( -10) - 4 * 1 * q

100 - 4q = 0

-4q = -100

q = -100/ -4

q = 25

Hence, The value of q = 25 $.$