Question Solve the quadratic equation $8 x^{2} = 7 x - 5$ and compute its discriminant.

Studdy Solution

STEP 1

Assumptions
1. The given equation is $8x^2 = 7x - 5$ .
2. The standard form of a quadratic equation is $ax^2 + bx + c = 0$ .
3. The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$ .
4. We need to rewrite the given equation in the standard form to compute the discriminant.

STEP 2

First, we need to rewrite the given equation in standard form by bringing all terms to one side of the equation.
$8x^2 - 7x + 5 = 0$

STEP 3

Identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation.
In our equation, $a = 8$ , $b = -7$ , and $c = 5$ .

STEP 4

Now, we will use the formula for the discriminant $D = b^2 - 4ac$ to compute the discriminant of the given quadratic equation.

STEP 5

Substitute the values of $a$ , $b$ , and $c$ into the discriminant formula.
$D = (-7)^2 - 4(8)(5)$

STEP 6

Calculate the square of $b$ .
$(-7)^2 = 49$

STEP 7

Calculate the product of $4$ , $a$ , and $c$ .
$4(8)(5) = 160$

STEP 8

Subtract the product of $4ac$ from $b^2$ to find the discriminant.
$D = 49 - 160$

STEP 9

Compute the discriminant.
$D = 49 - 160 = -111$
The discriminant of the quadratic equation $8x^2 = 7x - 5$ is $-111$ .

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Question Solve the quadratic equation $8 x^{2} = 7 x - 5$ and compute its discriminant.

Studdy Solution

STEP 1

STEP 2

First, we need to rewrite the given equation in standard form by bringing all terms to one side of the equation.
$8x^2 - 7x + 5 = 0$

STEP 3

Identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation.
In our equation, $a = 8$ , $b = -7$ , and $c = 5$ .

STEP 4

Now, we will use the formula for the discriminant $D = b^2 - 4ac$ to compute the discriminant of the given quadratic equation.

STEP 5

Substitute the values of $a$ , $b$ , and $c$ into the discriminant formula.
$D = (-7)^2 - 4(8)(5)$

STEP 6

Calculate the square of $b$ .
$(-7)^2 = 49$

STEP 7

Calculate the product of $4$ , $a$ , and $c$ .
$4(8)(5) = 160$

STEP 8

Subtract the product of $4ac$ from $b^2$ to find the discriminant.
$D = 49 - 160$

STEP 9

Compute the discriminant.
$D = 49 - 160 = -111$
The discriminant of the quadratic equation $8x^2 = 7x - 5$ is $-111$ .

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Question Solve the quadratic equation 8x2=7x−58 x^{2} = 7 x - 58x2=7x−5 and compute its discriminant.

Studdy Solution

STEP 1

STEP 2

First, we need to rewrite the given equation in standard form by bringing all terms to one side of the equation.8x2−7x+5=08x^2 - 7x + 5 = 08x2−7x+5=0

STEP 3

Identify the coefficients aaa, bbb, and ccc from the standard form of the quadratic equation.In our equation, a=8a = 8a=8, b=−7b = -7b=−7, and c=5c = 5c=5.

STEP 4

Now, we will use the formula for the discriminant D=b2−4acD = b^2 - 4acD=b2−4ac to compute the discriminant of the given quadratic equation.

STEP 5

Substitute the values of aaa, bbb, and ccc into the discriminant formula.D=(−7)2−4(8)(5)D = (-7)^2 - 4(8)(5)D=(−7)2−4(8)(5)

STEP 6

Calculate the square of bbb.(−7)2=49(-7)^2 = 49(−7)2=49

STEP 7

Calculate the product of 444, aaa, and ccc.4(8)(5)=1604(8)(5) = 1604(8)(5)=160

STEP 8

Subtract the product of 4ac4ac4ac from b2b^2b2 to find the discriminant.D=49−160D = 49 - 160D=49−160

STEP 9

Compute the discriminant.D=49−160=−111D = 49 - 160 = -111D=49−160=−111The discriminant of the quadratic equation 8x2=7x−58x^2 = 7x - 58x2=7x−5 is −111-111−111.

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Question Solve the quadratic equation $8 x^{2} = 7 x - 5$ and compute its discriminant.

First, we need to rewrite the given equation in standard form by bringing all terms to one side of the equation.
$8x^2 - 7x + 5 = 0$

Identify the coefficients $a$ , $b$ , and $c$ from the standard form of the quadratic equation.
In our equation, $a = 8$ , $b = -7$ , and $c = 5$ .

Now, we will use the formula for the discriminant $D = b^2 - 4ac$ to compute the discriminant of the given quadratic equation.

Substitute the values of $a$ , $b$ , and $c$ into the discriminant formula.
$D = (-7)^2 - 4(8)(5)$

Calculate the square of $b$ .
$(-7)^2 = 49$

Calculate the product of $4$ , $a$ , and $c$ .
$4(8)(5) = 160$

Subtract the product of $4ac$ from $b^2$ to find the discriminant.
$D = 49 - 160$

Compute the discriminant.
$D = 49 - 160 = -111$
The discriminant of the quadratic equation $8x^2 = 7x - 5$ is $-111$ .