Write the discriminant of the following quadratic equations:

$(x+5)^2=2(5x-3)$

Given:

Given quadratic equation is $(x+5)^2=2(5x-3)$.

To do:

We have to find the discriminant of the given quadratic equation.

Solution:

$(x+5)^2=2(5x-3)$

$x^2+2(x)(5)+(5)^2=2(5x)-2(3)$

$x^2+10x+25=10x-6$

$x^2+10x-10x+25+6=0$

$x^2+31=0$

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=1, b=0$ and $c=31$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

Therefore,

$D=(0)^2-4(1)(31)=0-124=-124$.

The discriminant of the given quadratic equation is $-124$.

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Updated on: 10-Oct-2022

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