Question

The values of a, b, and c of a quadratic equation written in standards from are -2,8, and 3, respectively. Another quadratic equation has 2, -8, and -3 as the values of a, b, and c, respectively. Do you agree that the two equations have the same solutions? Justify your answer.

Answer 1

SOLUTION

GIVEN

• The values of a, b, and c of a quadratic equation written in standards from are -2,8, and 3, respectively.

• Another quadratic equation has 2, -8, and -3 as the values of a, b, and c, respectively.

TO JUSTIFY

• To The whether two equations have the same solutions

• TO Justify the answer

EVALUATION

The standard form of a quadratic equation is

$\sf{a {x}^{2} + bx + c = 0\: } \: \: ......(1)$

$\sf{Where \: a, b, c \: are \: real \: number \: with \: a \ne 0 }$

EQUATION TO FIRST QUESTION

Here it is given that a = - 2, b = 8 & c = 3

So From Equation (1) we get

$\sf{ - 2 {x}^{2} + 8x + 3 = 0}$

Multiplying both sides by (-1) we get

$\sf{2 {x}^{2} - 8x - 3 = 0 } \: \: .....(2)$

EQUATION TO SECOND QUESTION

Here it is given that a = 2, b = - 8, c = - 3

So From Equation (1) we get

$\sf{2 {x}^{2} - 8x - 3 = 0 } \: \: .....(3)$

JUSTIFICATION

We are observing that the two equations in Equation (2) & Equation (3) are same

Since the two equations are same,

So the two equations have the same roots

Hence the two equations have the same solutions

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