Question

find the zeroes of the following quadratic polynomial and verify the relationship question no 1 part 6 3x^2-x-4

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Answer 1

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Answer 2

Given:-

• p(x) = 3x² - x - 4

To find:-

• Zeroes of p(x)

To verify:-

• Relation between the zeroes and coefficient of the polynomial.

Answer:-

Given that,

p(x) = 3x² - x - 4

Splitting the middle term,

→ p(x) = 3x² - 4x + 3x - 4

→ p(x) = x(3x - 4) + 1(3x - 4)

→ p(x) = (3x - 4)(x + 1)

For finding zeroes, the value of p(x) should be zero on substituting the zero in place of x.

→ (3x - 4)(x + 1) = 0

Either (3x - 4) = 0

or (x + 1) = 0

If (3x - 4) = 0:

→ 3x = 4

→ x₁ = 4/3

If (x + 1) = 0

→ x₂ = -1

Hence, the zeroes are,

• x₁ = 4/3
• x₂ = -1

Verification:

We know that if the polynomial ax² + bx + c are x₁ and x₂, then,

• x₁ + x₂ = -b/a
• x₁x₂ = c/a

So,

x₁ + x₂ = -b/a

→ 4/3 + (-1) = -(-1/3)

→ 1/3 = 1/3

L.H.S. = R.H.S.

Hence verified!

And,

x₁x₂ = c/a

→ (4/3) * (-1) = -4/3

→ -4/3 = -4/3

L.H.S. = R.H.S.

Hence verified!