Question

If α and β are zeros of the polynomial x2 + 5x + 6, then what is the value of α + β?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\alpha+\beta=-5}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} +5x+6 = 0 \\ \\ \tt: \implies \alpha \: and \: \beta \: are \: the \: zeores \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies { \alpha } + { \beta } = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {x}^{2} + 5x + 6 = 0 \\ \\ \tt: \implies {x}^{2} + 3x + 2x + 6 = 0 \\ \\ \tt: \implies x(x + 3) + 2(x + 3) = 0 \\ \\ \tt: \implies (x + 3)(x + 2) = 0 \\ \\ \green{\tt: \implies x = - 3 \: and \: - 2} \\ \\ \tt \circ \: \alpha = - 3 \\ \\ \tt \circ \: \beta = - 2 \\ \\ \bold{For \: finding \: value : } \\ \tt : \implies \alpha + \beta \\ \\ \tt : \implies - 3 - 2 \\ \\ \green{\tt : \implies - 5} \\ \\ \green{\tt \therefore \alpha + \beta = - 5} \\ \\ \bold{Alternate \: method : } \\ \tt : \implies Sum \: of \: zeroes = \frac{ - b}{a} \\ \\ \tt : \implies \alpha + \beta = \frac{ - 5}{1} \\ \\ \green{\tt : \implies \alpha + \beta = - 5}$

Answer 2

QUESTION :

If α and β are zeros of the polynomial x2 + 5x + 6, then what is the value of α + β?

SOLUTION :

Sum of the Zeroes of a polynomial is equal to -b/a

From the given Polynomial we can find that :

b = 5

a = 1

-b/a = -5

Hence the answer was -5.