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What is the discriminant of the quadratic equation
4x^(2)-7x+1=0 ?
33

-65

-33
65

What is the discriminant of the quadratic equation $4 x^{2}-7 x+1=0$ ? $\newline$ $33$ $\newline$ $-65$ $\newline$ $-33$ $\newline$ $65$

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Solve exponential equations by rewriting the base

Full solution

Q. What is the discriminant of the quadratic equation

4 x^{2}-7 x+1=0

?

\newline

33

\newline

-65

\newline

-33

\newline

65

Identify Coefficients: The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by the formula $D = b^2 - 4ac$ . Let's identify the coefficients $a$ , $b$ , and $c$ from the given equation $4x^2 - 7x + 1 = 0$ .
Calculate Coefficients: The coefficient $a$ is the coefficient of $x^2$ , which is $4$ . The coefficient $b$ is the coefficient of $x$ , which is $-7$ . The coefficient $c$ is the constant term, which is $1$ .
Plug into Formula: Now we will plug these values into the discriminant formula $D = b^2 - 4ac$ . So we have $D = (-7)^2 - 4(4)(1)$ .
Calculate Discriminant: Calculating the discriminant, we get $D = 49 - 16$ . We square $-7$ to get $49$ and multiply $4$ by $4$ and then by $1$ to get $16$ .
Final Result: Subtracting $16$ from $49$ , we get $D = 33$ . This is the value of the discriminant.

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