Question

Find a quadratic polynomial ,the sum and product of whose zeroes are 2/5 and 21

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Answer 1

Answer:

$\huge\underline\mathcal\red{AnSWer}$

Let the given polynomial be p(x) = 4x2 – 4x – 8

To find the zeroes, take p(x) = 0

Now, factorise the equation 4x2 – 4x – 8 = 0

4x2 – 4x – 8 = 0

4(x2 – x – 2) = 0

x2 – x – 2 = 0

x2 – 2x + x – 2 = 0

x(x – 2) + 1(x – 2) = 0

(x – 2)(x + 1) = 0

x = 2, x = -1

So, the roots of 4x2 – 4x – 8 are -1 and 2.

Relation between the sum of zeroes and coefficients:

-1 + 2 = 1 = -(-4)/4 i.e. (- coefficient of x/ coefficient of x2)

Relation between the product of zeroes and coefficients:

(-1) × 2 = -2 = -8/4 i.e (constant/coefficient of x2)