Question

If the quadratic equation px\frac{1}{2} – 25–√ px + 15 = 0 has two equal roots, then find

the value of p.​

Answer 1

Step-by-step explanation:

If in equation ax

2

+bx+c=0 the two roots are equal

Then b

2

−4ac=0

In equation px

2

−2

5

px+15=0

a=p,b=−2

5

p and c=15

Then b

2

−4ac=0

⇒(−2

5

p)

2

−4×p×15=0

⇒20p

2

−60p=0

⇒20p(p−3)=0

So when p−3=0⇒p=3

p



=0 as it makes coefficient of x

2

=0

Hence, p=3

Answer 2

ANSWER

Given quadratic equation is, px² -2√5

px + 15 = 0

Compare px² - 2√5 px+ 15 = 0 with

ax²+ bx+ c = 0

a = p, b = - 2√5 p , c = 15

We know that, If the roots of the quadratic equation are equal, then it's discriminant (D) equals to zero. discriminant = 0

b² - 4ac = 0

(- 2√5 p)² - 4 x p x 15 = 0

20p² - 60p = 0

20p (p - 3) = 0

p - 3 = 0

p = 3