Question

Find the value of p for which the equation px2 - 8x+4 =0 has two equal roots.

Answer 1

quadratic eq has two equal roots.

when det =0

b^2-4ac=0

ax^2+bx+c=0

comparing to px^2-8x+4=0

p=a   ,   b=-8    ,   c=4

b^2-4ac=0

64-4(p)(4)=0

64-16p=0

p=4

Answer 2

Concept

The discriminant is  part of the quadratic equation below the square root. The discriminant is either positive, zero, or negative and  determines how many solutions there are for a given quadratic equation.

A positive discriminant indicates that the square has two different real  solutions.

A discriminant of zero indicates that the square has a repeating real  solution.

Negative discriminant indicate that none of the solutions are real.

Given

We have given a quadratic equation  $px^2-8x+4=0$ and this equation has two equal roots.

Find

We are asked to determine the value of p in the given equation.

Solution

For equal roots, discriminant is zero which is given by  $b^2-4ac$ ...(1)

On comparing with the given equation $px^2-8x+4=0$ , we get

a = p , b = -8 and c = 4

Putting above values in equation (1) , we get

$b^2-4ac=0\\(-8)^2-4(p)(4)=0\\64-16p=0\\16p=64\\p=4$

Hence the value of p is 4 for which the given equation has equal roots.

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