Question

Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial​

Answer 1

Step-by-step explanation:

Given Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial

• Now we have P(x) = x^2 – (sum of roots)x + product of roots. --------1
• Now sum of roots = α + β = -2 – 5 = - 7
• Product of roots = αβ = - 2 x – 5 = 10
• Substituting these values in equation 1 we get
•  P(x) = x^2 – (- 7) x + 10
•         = x^2 + 7x + 10 -------------2
•        = x^2 + 5x + 2x + 10
•       = x(x + 5) + 2(x + 5)
•       = (x + 5)(x + 2)
• Now putting P(x) = 0 we get
•      (x + 5) (x + 2) = 0
• So x + 5 = 0 , x + 2 = 0
• So x = - 5, - 2
• So these are the given roots.
• Now sum of roots = - b/a  (from equation 2)
•                              = - 7 / 1
•                             = - 7
• Also product of roots = c/a
•                                     = 10 / 1
•                                    = 10
• Therefore the relation satisfies the coefficients of the polynomial.

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