Question

find a quadratic polynomial the sum and product of whose zeroes are 4 and 1 respectively​

Answer 1

$\bf{\underline{Solution}}:-$

Let α and β be the zeros of the quadratic Polynomial f(x)

➝ α + β = 4

➝ α × β = 1

Now,

f(x) = x² - (α + β)x + (α × β)

➝ f(x) = x² - (4)x + 1

➝ f(x) = x² - 4x + 1

Hence,the quadratic polynomial will be x² - 4x + 1.

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✝ Related to quadratic polynomial :-

If α and β are the zeros of p(x) = ax² + bx + c where a ≠ 0 then,

• α + β = -b/a

• α × β = c/a

✝ Related to Cubic polynomial :-

If α,β and γ are the zeros of p(x) = ax³ + bx² + cx + d then,

• (α + β + γ) = -b/a

• (αβ + βγ + γα) = c/a

• α × β × γ = -d/a