QuestionFind the Discriminant of the quadratic equation $y=3 x^{2}-5 x+2$ .

Studdy Solution

STEP 1

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

STEP 2

The Discriminant of a quadratic equation is given by the formula $= b^{2} -4ac$

STEP 3

Now, plug in the given values for $a$ , $b$ , and $c$ into the formula to calculate the Discriminant.
$= (-5)^{2} -32$

STEP 4

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

STEP 5

Calculate the product of $4$ , $3$ , and $2$ .
$432 =24$

STEP 6

Subtract the product from the square to find the Discriminant.
$=25 -24$

STEP 7

Calculate the Discriminant.
$=25 -24 =1$ The Discriminant of the given quadratic equation is1.

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QuestionFind the Discriminant of the quadratic equation $y=3 x^{2}-5 x+2$ .

Studdy Solution

STEP 1

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

STEP 2

The Discriminant of a quadratic equation is given by the formula $= b^{2} -4ac$

STEP 3

Now, plug in the given values for $a$ , $b$ , and $c$ into the formula to calculate the Discriminant.
$= (-5)^{2} -32$

STEP 4

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

STEP 5

Calculate the product of $4$ , $3$ , and $2$ .
$432 =24$

STEP 6

Subtract the product from the square to find the Discriminant.
$=25 -24$

STEP 7

Calculate the Discriminant.
$=25 -24 =1$ The Discriminant of the given quadratic equation is1.

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QuestionFind the Discriminant of the quadratic equation y=3x2−5x+2y=3 x^{2}-5 x+2y=3x2−5x+2.

Studdy Solution

STEP 1

Assumptions1. The given equation is a quadratic equation of the form ax+bx+c=0ax^{} + bx + c =0ax+bx+c=0. . The coefficients are a=3a =3a=3, b=−5b = -5b=−5, and c=c =c=.

STEP 2

The Discriminant of a quadratic equation is given by the formula=b2−4ac = b^{2} -4ac=b2−4ac

STEP 3

Now, plug in the given values for aaa, bbb, and ccc into the formula to calculate the Discriminant.=(−5)2−∗3∗2 = (-5)^{2} -*3*2=(−5)2−∗3∗2

STEP 4

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

STEP 5

Calculate the product of 444, 333, and 222.4∗3∗2=244*3*2 =244∗3∗2=24

STEP 6

Subtract the product from the square to find the Discriminant.=25−24 =25 -24=25−24

STEP 7

Calculate the Discriminant.=25−24=1 =25 -24 =1=25−24=1The Discriminant of the given quadratic equation is1.

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QuestionFind the Discriminant of the quadratic equation $y=3 x^{2}-5 x+2$ .

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

The Discriminant of a quadratic equation is given by the formula $= b^{2} -4ac$

Now, plug in the given values for $a$ , $b$ , and $c$ into the formula to calculate the Discriminant.
$= (-5)^{2} -32$

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

Calculate the product of $4$ , $3$ , and $2$ .
$432 =24$

Subtract the product from the square to find the Discriminant.
$=25 -24$

Calculate the Discriminant.
$=25 -24 =1$ The Discriminant of the given quadratic equation is1.