If alpha, beta are the zeroes of x^2+7x+10 find the polynomial whose zeroes are 5 alpha and 5 beta
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Answer:
x²+35x+250= 0
Step-by-step explanation:
x² + 7x +10 = 0
x² +5x+2x+10= 0
x(x+5) +2(x+5) = 0
(x+5)(x+2)=0
The roots of the given equation alpha and beta are -5 and - 2 respectively.
now we have to find the equation whose roots are -25 and -10.
The equation is
x² - ( -25-10) x + ( -25×-10)= 0
x²-(-35)x +250 = 0
x²+35x+250= 0
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