Question

find the zeroes of polynomials x³+3x-10 and verify the relation between its zeroes and coefficients.​

Answer 1

By factoring x² + 3x - 10,

x² + 3x - 10

= x² + (5 - 2)x - 10

= x² + 5x - 2x - 10

= x(x + 5) - 2(x + 5)

= (x + 5)(x - 2).

So, zeroes are (- 5), (+ 2).

Now, we know Vieta's formulae:-

• α + β = - b/a
• αβ = c/a

for any quadratic polynomial in form of ax² + bx + c where a ≠ 0 and α, β are its zeroes.

So,

1. Sum: (- 5) + (+ 2) = - 3 = - (+ 3)/(+ 1) = - b/a.
2. Product: -5 . 2 = - 10 = (- 10)/(1) = c/a.

So, verified.