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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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