QuestionFind the Discriminant of the equation $y=5 x^{2}-5 x+10$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is a quadratic equation of the form $ax^{} + bx + c =0$ . The coefficients are $a =5$ , $b = -5$ , and $c =10$
3. The Discriminant of a quadratic equation is given by the formula $= b^{} -4ac$

STEP 2

We need to find the Discriminant of the given quadratic equation. We can do this by substituting the values of $a$ , $b$ , and $c$ into the formula for the Discriminant.
$= b^{2} -4ac$

STEP 3

Now, plug in the given values for $a$ , $b$ , and $c$ to calculate the Discriminant.
$= (-5)^{2} -510$

STEP 4

Calculate the square of $-$ .
$(-)^{2} =25$

STEP 5

Substitute $25$ back into the Discriminant formula.
$=25 -4510$

STEP 6

Calculate the product of $4$ , $5$ , and $10$ .
$4510 =200$

STEP 7

Substitute $200$ back into the Discriminant formula.
$=25 -200$

STEP 8

Calculate the Discriminant.
$=25 -200 = -175$ The Discriminant of the given quadratic equation is $-175$ .

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