The quadratic polynomial whose sum of the zeroes is 3 and product of the zeroes – 2 is a) 2 x x 3 2 b) 2 x x 2 3 c) 2 x x 3 2 d) 2 x x 3 2
Answers
Answer:
Answer (1) :-
→ sum of zeroes = 3
→ Product of zeroes = (-2) .
we know that, when we have given sum & product of zeros of a quadratic polynomial , than the equation will be :- x² - (sum of Roots)x + Product of Roots = 0
Putting Both values we get :-
→ x² - 3x + (-2) = 0
→ x² - 3x - 2 = 0 (Ans.)
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Answer (2) :-
Given that :-
→ (X+1) is a factor of 2×3+ax2 + 2bx+1 => ax² + 2bx + 6 + 1 => ax² + 2bx + 7
and,
→ 2a - 3b = 4 -------------- Equation (1).
we know that, when (x +a) is a factor of given Polynomial, than f(-a) will give Remainder as Zero.
→ x + 1 = 0
→ x = (-1)
So,
→ f(-1) = ax² + 2bx + 7
→ 0 = a(-1)² + 2b(-1) + 7
→ 0 = a - 2b + 7
→ a - 2b = (-7) ------------ Equation (2).
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Multiply Equation (2) by 2 , and Than, subtracting it from Equation (1) , we get,
→ (2a - 3b) - 2(a - 2b) = 4 - 2(-7)
→ 2a - 2a - 3b + 4b = 4 + 14
→ b = 18 (Ans.)
Putting value of b in Equation (1) now,
→ 2a - 3*18 = 4
→ 2a = 4 + 54
→ 2a = 58
→ a = 29 (Ans.)
Hence, value of a & b are 29 & 18 Respectively.
Step-by-step explanation:
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