Question

If the sum and product of the zero of a quadratic polynomial are - 1 by 2 and minus 3 respectively then the required quadratic polynomial is

Answer 1

ANSWER :–

▪︎2x² + x - 6 = 0

EXPLANATION :–

GIVEN :–

▪︎ Sum of roots = -(½)

▪︎ Product of roots = -3

TO FIND :–

Quadratic polynomial.

SOLUTION :–

▪︎ We know that a quadratic polynomial in form of Sum of roots and product of roots is –

$\\ \implies { \boxed{ \bold{{ {x}^{2} - (sum \: \: of \: \: roots)x +( product \: \: of \: \: roots) = 0}}}}$

$\\ \implies { \bold{{ {x}^{2} - ( - \frac{1}{2} )x +( - 3) = 0}}}$

$\\ \implies { \bold{{ {x}^{2} + \frac{1}{2} x - 3 = 0}}}$

$\\ \implies { \boxed{\bold{{ 2{x}^{2} + x - 6 = 0}}}}$

VERIFICATION :–

▪︎ If a quadratic equation ax² + bx + c = 0 then –

$\\ \: \: . \: \: { \bold{sum \: \: of \: \: roots = - \frac{b}{a} }}$

$\\ \: \: \implies \: \: { \bold{ - \frac{1}{2} = - \frac{1}{2} (verified)}}$

$\\ \: \: . \: \: { \bold{product\: \: of \: \: roots = \dfrac{c}{a} }}$

$\\ \: \: \implies \: \: { \bold{ - 3 = \dfrac{ - 6}{2} }}$

$\\ \: \: \implies \: \: { \bold{ - 3 = - 3(verified)}}$

Answer 2

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$\huge\tt{GIVEN:}$

• The sum of zero of a quadratic polynomial is -1 by 2
• The product of zero of a quadratic polynomial is -3

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$\huge\tt{TO~FIND:}$

• The required polynomial

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$\huge\tt{SOLUTION:}$

We know,

↪x²-(sum of roots)x+ (product of roots)

↪x² - (-½)x + (-3) = 0

↪x² + ½x - 3 = 0

↪ 2x² + x - 6 = 0

Hence, 2x² + x - 6 = 0 would be the required polynomial

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