Find the quadratic polynomial, the sum of whose zeroes is -5 and their

1.	Find the quadratic polynomial, the sum of whose zeroes is -5 and their product is 6.
Answer» Let the required quadratic polynomial is ax² + bx + c. … (1) Therefore, Sum of zeros is \(-\frac{b}{a}\) = −5 (given) ⇒ b = 5a. And product of zeros is \(\frac{c}{a}\) = 6 (given) ⇒ c = 6a. By putting the values of b and c in equation (1), we get the quadratic polynomial. ax² + 5ax +6a = a(x² + 5x + 6) Where a is any real number except zero. Hence, The required polynomial is a(x²+5x+6), a ≠ 0, a∈R.

Find the quadratic polynomial, the sum of whose zeroes is -5 and their product is 6.

Answer»

Let the required quadratic polynomial is ax² + bx + c. … (1)

Therefore,

Sum of zeros is \(-\frac{b}{a}\) = −5 (given)

⇒ b = 5a.

And product of zeros is \(\frac{c}{a}\) = 6 (given)

⇒ c = 6a.

By putting the values of b and c in equation (1), we get the quadratic polynomial.

ax² + 5ax +6a = a(x² + 5x + 6)

Where a is any real number except zero.

Hence,

The required polynomial is a(x²+5x+6), a ≠ 0, a∈R.

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Find the quadratic polynomial, the sum of whose zeroes is -5 and their product is 6.

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