Math, asked by hemanthgowdamd, 4 months ago


Find the values of p for which the equation (p - 12) x² + 2 (p-12) x + 2 = 0 has two equal roots.


Answers

Answered by tennetiraj86
3

Step-by-step explanation:

Given:-

The quadratic equation (p - 12) x² + 2 (p - 12) x + 2 = 0 has two equal roots.

To find:-

Find the values of p ?

Solution:-

Given quadratic equation is (p - 12) x² + 2 (p - 12) x + 2 = 0

On comparing with the standard quadratic

equation ax² + bx + c = 0

We have,

a = (p - 12)

b = 2 (p - 12)

c = 2

Since it has two equal roots then it's discriminant must be zero.

=> b² - 4ac = 0

=> [ 2 (p - 12) ]² - 4 (p - 12)(2) = 0

=> 4(p - 12)² - 8 (p - 12) = 0

=> 4[(p - 12)² - 2(p - 12)] = 0

=> (p - 12)² - 2(p - 12) = 0/4

=> (p - 12)² - 2(p - 12) = 0

=>(p - 12)[(p - 12) - 2] = 0

=>(p - 12)(p - 14) = 0

=>p - 12 = 0 or p - 14 = 0

=>p = 12 or p = 14

If p = 12 then the given quadratic equation does not exist.

Therefore, P = 14

Answer:-

The value of p for the given problem = 14

Used formulae:-

If the discriminant of the quadratic equation is zero then it has two equal roots.

ax²+bx+c=0 is the quadratic equation then it's

discriminant is D=b²-4ac.

If D=0 then it has real and two equal roots.

If D>0 then it has two distinct and real roots.

If D<0 then it has no real roots.

Answered by UniqueBabe
3

Answer

(p−12)x

2

−2(p−12)x+2=0

For quadratic equation to has equal roots

b

2

=4ac

4(p−12)

2

=4(p−12)(2)

p−12=2

p=2+12

p=14

Similar questions