Question

sum of the roots of the quadratic equation x²+3x-28=0​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ x² + 3x - 28 = 0.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ α + β = -(3)/1 = - 3.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ αβ = (-28)/1 = - 28.

                                                                                                                       

MORE INFORMATION.

Cubic polynomial.

Sum of the zeroes of the cubic polynomial.

⇒ α + β + γ = - b/a.

Products of the zeroes of the cubic polynomial two at a time.

⇒ αβ + βγ + γα = c/a.

Products of the zeroes of the cubic polynomial.

⇒ αβγ = - d/a.

Formula of cubic polynomial.

⇒ x³ - (α + β + γ)x² + (αβ + βγ + γα)x - αβγ.

Answer 2

$\large\bf\underline\red{Answer \: :-}$

Given equation : x² + 3x - 28 = 0

By Factorisation,

$\sf\longrightarrow{x {}^{2} + 7x - 4x - 28 = 0 } \\ \\ \sf\longrightarrow{x(x + 7) - 4(x + 7) = 0} \\ \\ \sf\longrightarrow{(x + 7)(x - 4) = 0} \\ \\ \sf\longrightarrow{x + 7 = 0} \\ \sf\longrightarrow \pink{x = - 7} \: \: \: \: \: \\ \\ \sf\longrightarrow{x - 4 = 0} \\ \sf\longrightarrow \pink{x = 4} \: \: \: \: \: \: \:$

Roots of the equation :

⚫ x = -7

⚫ x = 4

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