Question

13.) Find a quadratic polynomial whose zeros are 1 and -3. Verify the relation between the coefficients and zeros of the polynomial. (2)​

Answer 1

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

• The zeroes of quadratic equation are 1 and - 3

We know that ,

$\mathtt{ \fbox{ \large{(x)}^{2} - (sum \: of \: roots)x + (product \: of \: roots)}}$

Thus ,

(x)² - (1 + (-3))x + ( 1 × (-3))

(x)² + 2x - 3

Hence , the required polynomial is (x)² + 2x - 3

$\mathtt{ \huge{ \fbox{</strong><strong>Verification</strong><strong> :)}}}$

We know that ,

$\large \mathtt{ \fbox{Sum \: of \: roots = - \frac{b}{a} }}$

Thus ,

1 + (-3) = - 2/1

-2 = -2

And

$\large \mathtt{ \fbox{Product \: of \: roots = \frac{c}{a} }}$

Thus ,

1 × (-3) = -3/1

-3 = -3

Hence verified

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