Final Answer
$9$
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Step-by-step Solution
Specify the solving method
1
The discriminant (D) of a quadratic polynomial of the form $ax^2+bx+c$ is calculated using the following formula, where $a$, $b$ and $c$ are the coefficients of the corresponding terms
$D=b^2-4ac$
2
From the equation, we see that $a=-1$, $b=7$ and $c=-10$. Replacing the values of $a$, $b$ and $c$ in the previous formula, we obtain
$D=7^2-1\cdot 4\cdot -1\cdot 1\cdot -10$
3
Multiply $-1$ times $4$
$7^2-4\cdot -1\cdot 1\cdot -10$
4
Multiply $-4$ times $-1$
$7^2+4\cdot 1\cdot -10$
5
Multiply $4$ times $1$
$7^2+4\cdot -10$
6
Multiply $4$ times $-10$
$7^2-40$
7
Calculate the power $7^2$
$49-40$
8
Subtract the values $49$ and $-40$
$9$
9
The discriminant of the polynomial results in
$9$
Final Answer
$9$