Find a quadratic polynomial whose zeros are -5 and -7 – InterviewSolution

1.

Find a quadratic polynomial whose zeros are -5 and -7

Answer»

$\boxed{\mathfrak\purple{<klux>QUADRATIC</klux> \: <klux>EQUATION</klux> \: is \: {x}^{2} + 12x + <klux>35</klux> = 0}}$

Given:

Quadratic equation has zeroes -5 & -7.

To Find:

The quadratic equation.

Solution:

LET us assume,

$\mathfrak{ \alpha = - 5}$

$\mathfrak{ \beta = - 7}$

Now,

$\star \: \pink{\underline{\mathfrak{ \alpha + \beta = }}}$

$\\ \\ \\ :\implies\mathfrak{( - 5) + ( - 7)} \\ \\ \\ \\ \\ :\implies\mathfrak{ - 5 - 7} \\ \\ \\ \\ \boxed{:\implies\mathfrak\blue{ - 12}}$

$\star \: \pink{\underline{\mathfrak{ \alpha \times \beta = }}}$

$\\ \\ \\ :\implies\mathfrak{( - 5) \times ( - 7)} \\ \\ \\ \\ \\ \boxed{:\implies\mathfrak\orange{35}}$

We know that,

$\star \: \boxed{\mathfrak\green{Obtaining \: quadratic \: equation = {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0}}$

Placing values,

$:\implies\mathfrak{ {x}^{2} - ( - 12) \times x + 35 = 0} \\ \\ \\ \\ \\ :\implies\mathfrak{ {x}^{2} + 12 \times x + 35 = 0} \\ \\ \\ \\ \\ \\ \\ \star\sf \: \underbrace\red{ {x}^{2} + 12x + 35 = 0} \: \star$

Quadratic equation formed is x² + 12x + 35 = 0.

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