Question

Find all the common zeroes of the polynmials : p(x) = x3 + 5x2 – 9x – 45 and g(x) = x3 + 8x2 + 15x

Answer 1

I hope this helps , just subtract the 2 eqns and find the root of the resulting eqns and that will be your ans

Answer 2

we have to find the common zeroes of the polynomials :

• P(x) = x³ + 5x² - 9x - 45
• g(x) = x³ + 8x² + 15x

compute x at P(x) = g(x)

⇒ x³ + 5x² - 9x - 45 = x³ + 8x² + 15x

⇒5x² - 9x - 45 = 8x² + 15x

⇒3x² + 24x + 45 = 0

⇒x² + 8x + 15 = 0

⇒x² + 3x + 5x + 15 = 0

⇒x(x + 3) + 5(x + 3) = 0

⇒(x + 5)(x + 3) = 0

⇒x = -3, -5

hence common zeroes of the polynomials are -3 and -5.

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