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5.

Find the zeroes of the quadratic polynomial P(x) = x2 + x-12 and

verify the relationship between the zeroes and the c

Question

5.

Find the zeroes of the quadratic polynomial P(x) = x2 + x-12 and

verify the relationship between the zeroes and the coefficients.

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Mathematics
3 months
2021-07-06T15:31:15+00:00
2021-07-06T15:31:15+00:00 2 Answers
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## Answers ( )

EXPLANATION.Quadratic equation.

⇒ x² + x – 12.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -(1)/1 = -1.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = (-12)/1 = -12.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ x² + x – 12 = 0.

⇒ x² + 4x – 3x – 12 = 0.

⇒ x(x + 4) – 3(x + 4) = 0.

⇒ (x – 3)(x + 4) = 0.

⇒ x = 3 and x = -4.

Sum of the values of x, we get.

⇒ 3 + (-4) = -1.

Products of the values of x, we get.

⇒ (3)(-4) = -12.

MORE INFORMATION.Conditions for common roots.Let quadratic equation are a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0.

(1) = If only one roots is common.

⇒ x = b₁c₂ – b₂c₁/a₁b₂ – a₂b₁.

⇒ y = c₁a₂ – c₂a₁/a₁b₂ – a₂b₁.

(2) = If both roots are common.

⇒ a₁/a₂ = b₁/b₂ = c₁/c₂.

Answer:Given:–ToFind:–Relationship the zeroes and the coefficients.

Solution:–We know that

•SumofZeroes•ProductofZeroesLets factorise

Either

Or,

By putting the value

3 + (-4)

3 – 4

= -1

And,

3(-4)

-12