Question

If product of the zeroes of quadratic polynomial f(x) = x2 – x – m is –12, then find the value of m.

Answer 1

$\large\underline{\sf{Solution-}}$

Given polynomial is

$\red{\rm :\longmapsto\: {x}^{2} - x - m \: is \: such \: that \: product \: of \: zeroes \: is \: - 12}$

We know that

$\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

So, on substituting the values, we get

$\rm :\longmapsto\: - 12 = \dfrac{ - m}{1}$

$\rm :\longmapsto\: - 12 = - m$

$\rm :\longmapsto\: 12 = m$

$\rm \implies\:\boxed{\tt{ m \: = \: 12 \: }}$

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More to know

$\red{\rm :\longmapsto\: \alpha , \beta , \gamma \: are \: zeroes \: of \: a {x}^{3} + b {x}^{2} + cx + d, \: then}$

$\boxed{ \bf{ \: \alpha + \beta + \gamma = - \dfrac{b}{a}}}$

$\boxed{ \bf{ \: \alpha \beta + \beta \gamma + \gamma \alpha = \dfrac{c}{a}}}$

$\boxed{ \bf{ \: \alpha \beta \gamma = - \dfrac{d}{a}}}$

Answer 2

$\large\underline{\sf{Solution-}}$

Given polynomial is

$\red{\rm :\longmapsto\: {x}^{2} - x - m \: is \: such \: that \: product \: of \: zeroes \: is \: - 12}$

We know that

$\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

So, on substituting the values, we get

$\rm :\longmapsto\: - 12 = \dfrac{ - m}{1}$

$\rm :\longmapsto\: - 12 = - m$

$\rm :\longmapsto\: 12 = m$

$\rm \implies\:\boxed{\tt{ m \: = \: 12 \: }}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More to know

$\red{\rm :\longmapsto\: \alpha , \beta , \gamma \: are \: zeroes \: of \: a {x}^{3} + b {x}^{2} + cx + d, \: then}$

$\boxed{ \bf{ \: \alpha + \beta + \gamma = - \dfrac{b}{a}}}$

$\boxed{ \bf{ \: \alpha \beta + \beta \gamma + \gamma \alpha = \dfrac{c}{a}}}$

$\boxed{ \bf{ \: \alpha \beta \gamma = - \dfrac{d}{a}}}$