Math, asked by anupraj1482, 8 months ago

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

Answers

Answered by shinchanisgreat
4

Answer:

Quadratic Polynomial = x²+12x+35

Step-by-step explanation:

Refer to attached file for explanation.

Hope this answer helps you ^_^ !

Attachments:
Answered by ItzDαrkHσrsє
18

\boxed{\mathfrak\purple{Quadratic \: equation \: is \:  {x}^{2}  + 12x + 35 = 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

Hence,

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