Question

For what values of α the roots of the quadratic equation 5x2 + 2αx + 125 =0 are real and equal

Answer 1

Quadratic equation:

5x

2

−2kx+20=0

It is given that the roots of the quadratic equation are real and equal, Then discriminant D=0.

Comparing the given equation with ax

2

+bx+c=0

we have a=5,b=−2k and c=20

Now, D=0

∴b

2

−4ac=0

∴(−2k)

2

−4(5)(20)=0

∴4k

2

−400=0

∴k

2

=100

∴k=±10

Thus, k=10 or −10.

hope it helps you☺

Answer 2

Answer:

In the given equation

a = 5, b = 2a, and c = 125

We know,

when

$b {}^{2} - 4ac = 0$

then the roots of the equation are real and eaqual

So,

$b {}^{2} - 4ac = (2a) {}^{2} - 4 \times 5 \times 125 = 0 \\ 4a {}^{2} - 20 \times 125 = 0 \\ 4a {}^{2} - 1500 = 0 \\ 4a {}^{2} = 2500 \\ a {}^{2} = 625 \\ a = 25$

When,

the value of a is 25 then the given equation has real and equal roots.