Question

Find the quadratic polynomial whose zeroes are 2/3 and _1/4 . verify the relationship between the coefficients and zeroes of the polynomial

Answer 1

Hey mate here's your answer:
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Answer 2

Answer:

Step-by-step explanation:

Let α = 2/3 and β = 1/4

Quadratic polynomial is given by

p(x) = k ( x² - (α+β)x + αβ )

So, Sum of zeroes = α + β = 2/3 + 1/4 = 8/12 + 3/12 = 11/12

Product of zeroes = αβ = 2/3 × 1/4 = 1/6

So, p(x) = k ( x² - (11/12)x + 1/6 )

p(x) = 12k ( 12x² - 11x + 2 )

p(x) = K ( 12x² - 11x + 2 )

Now to verify the relation of coefficient and zeroes

p(x) = 12Kx² - 11Kx + 2K

$\frac{-coefficient\:of\:x}{coefficient\:of\:x^2}=\frac{-(-11K)}{12K}=\frac{11}{12}=Sum\:of\:zeroes$

$\frac{constant\:term}{coefficient\:of\:x^2}=\frac{2K}{12K}=\frac{1}{6}=Product\:of\:zeroes$