if alpha and beta are two zeroes of the polynomial x^2-5x+6 find a quadratic polynomial whose zeroes are 2alpha+1 and 2beta+1.
(With full and step by step explanation, brainliest will be chosen.)
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The correct answer is x²-12x+35=0.
Given: The equation = x²-5x+6=0
To Find: A quadratic polynomial whose zeroes are 2α+1 and 2β+1.
Solution:
x²-5x+6=0
= x²-3x-2x+6
= x(x-3) -2(x-3)
= (x-2)(x-3)
x=2,3
α = 2
β = 3
x² + (- sum of roots) + (product of roots) = 0
Roots are 2α + 1 and 2β + 1.
2α+1 = 2×2+1 = 5
2β+1 = 2×3+1 = 7
x²-(5+7)x+(5×7)=0
x²-12x+35=0
Hence, the equation is x²-12x+35=0.
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