Question

find 2kx2+6x+5=0 has Equal roots

Answer 1

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Answer 2

The value of k is $\frac{9}{10}$.

Given:

An equation $2kx^2+6x+5=0$.

To Find:

The value of k.

Solution:

The given equation is in the form of quadratic  $ax^2+bx+c=0$ and it has equal roots. In the case of equal roots, the discriminant of the quadratic equation is equal to zero.

The quadratic equation has three types of roots, these are real and equal roots, complex roots, and real and distinct roots.

Substitute $a=2k$, $b=6$, and $c=5$ into the formula of the discriminant$D={b^2-4ac}$.

$D={(6)^2-4(2k)(5)}$

Equate the value of the discriminant to zero and find k.

${6^2-4(2k)(5)}=0\\36-40k=0\\40k=36\\k=\frac{36}{40} \\=\frac{9}{10}$

Thus, the value of k is $\frac{9}{10}$.