Question

For what value of k, the quadratic equation 2kx-40x+25=0 has equal roots?Also, find the roots.​

Answer 1

Step-by-step explanation:

The given quadratic equation

$The \: given \: quadratic \: equation \: 2kx ^{2} - 40x + 25 = 0 \: comparing \: with \: a {x}^{2} + {b}x + c = 0$

⇒ We get, a=2k,b=−40 and c=25.

⇒ It is given that the roots are real and equal.

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

$( - 40) ^{2} - 4(2k)(25) = 0$

⇒ 1600−200k=0

⇒ 200k=1600

⇒ k=8

⇒ Hence, we have proved that given statement is true.

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Answer 2

Answer:

The answer will be;

• k = 8;
• Root of the polynomial = 5/4

Step-by-step explanation:

For equal roots we know a determinant and i.e,

b^2 - 4ac = 0;

Thus, (40)^2 - 4(2k)(25) = 0

1600 = 200k

k = 8.

Now, the quadratic equation is;

2(8)x^2 -40x+25=0;

16x^2 -40x+25=0;

Factorizing it;

16x^2 -20x -20x+25=0;

4x(4x - 5) - 5(4x - 5) = 0;

(4x - 5)(4x - 5) = 0;

Thus, the roots are;

4x - 5 =0

x = 5/4.

Both the roots are same. Thus, 5/4 and 5/4 are the roots.

That's all.