Question

Write quadratic equation
When
the sun
of roots is -7
and product is 5​

Answer 1

Step-by-step explanation:

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Answer 2

QuesTion:-

Write quadratic equation when sum of roots is -7 and product of roots is 5.

$\rule{200}2$

AnswEr:-

Your answer is $\tt x^2+7x+5=0.$

ExplanaTion:-

Given:-

• Sum of roots = -7.

• Product of roots = 5.

To Find:-

• The quadratic equation.

Concepts Used:-

• Every quadratic equation is in the form,

$\\ \tt\longrightarrow \: k[ {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0].$

• Sum of zeroes,

$\\ \tt\longrightarrow \: \alpha + \beta = \dfrac{ - b}{a}$

• Product of zeroes,

$\\ \tt\longrightarrow \alpha \beta = \dfrac{c}{a}$

Where,

• k is constant.

• $\tt \alpha$ And $\tt\beta$ Are zeroes of the equation.

• a Is Coefficient of x².

• -b Is - Coefficient of x.

• c Is Constant Term.

So here,

$\tt\mapsto \alpha + \beta = - 7 \\ \\ \tt \: and \\ \\ \tt\mapsto \alpha \beta = 5.$

Therefore the quadratic equation is:-

$\tt\mapsto k[ {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0]. \\ \\ \tt\mapsto {x}^{2} - ( - 7)x + (5) = 0. \\ \\ \tt(\because \:K \:\:is\:\: a\:\: constant)\\ \\ \tt\mapsto {x}^{2} + 7x + 5 = 0.$

$\therefore$ The required quadratic equation is x²+7x+5=0.