Question

find the zeroes of the quadratic polynomial P( x )=x²+x-12and verify the relationship between the zeroes and the coefficients
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Answer 1

Given -

Quadratic equation - x² + x - 12

To verify -

The relationship between the zeros of ther coefficients

Formulae used -

Sum of zeros, α + β = -b/a

Product of zeros, αβ = c/a

Solution -

In the question, we are provided with a quadratic equation, and we need to verify the relationship between their coefficients, for that, first we will do the middle term splitting of the given equation, then we will apply the formulae to verify the relationship. Let's do it!

Middle term splitting -

→ x² + x - 12

→ x² + 4x - 3x - 12

→ x(x + 4) - 3(x + 4)

→ (x + 4) (x - 3)

Now -

We will find the zeros of x + 4 and x - 3 and then we will solve the further question.

→ x + 4 = 0

→ x = 0 - 4

→ x = - 4 ------- (1st Zero)

→ x - 3 = 0

→ x = 0 + 3

→ x = 3 ------ (2nd zero)

Therefore, zeros are -4 and 3

Now -

For verifying the relationship between the coefficients, we will use apply 2 formulae here, and we have 2 sides, LHS and RHS. Here in LHS we will perform the actual addition and multiplication and in RHS we will use the formulae.

So -

α + β = coefficient of - x / coefficient of x²

LHS -

→ (3 - 4)

→ -1

RHS -

→ -1/1

→ -1

Hence, LHS = RHS

Secondly -

αβ = c/coefficient of x²

LHS -

→ 3 × -4

→ -12

RHS -

-12/1

or

→ -12

Hence, LHS = RHS

Answer 2

Answer:

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Step-by-step explanation:

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