Question

Please solve this question ​

Answer 1

Answer:

x^2 + 7x + 10 =0

x^2 + 5x +2x +10 = 0

x(x +5) + 2(x+5) = 0

(x+5) (x+2) =0

Applying zero product rule

if x +5 =0

x = -5

if x + 2 = 0

x = - 2

short cut method

alpha + beta = -b/a

where alpha and beta are roots of the equation

and b is the coefficient of x and a is the coefficient of x^2 . (quadratic equation generally is ax^2 + bx + c =0)

so -5 +(-2) = - (7(coefficient of x)) / (1 (coefficient of x^2))

-5-2 = -7

-7 = -7

LHS = RHS

hence Proved

Answer 2

x^2+7x+10=0

x^2+(5x+2x)+10=0

x^2+5x+2x+10=0

x(x+5)+2(x+5)=0

(x+5)(x+2)=0

Hence,zeros of a given quadratic polynomial are-5 and -2

Sum of zeros=-2+(-5)=-2-5

-7\1=-x coefficient \x^2 coefficient

product of zeros=(-2)(-5)

-10\1=constant\x^2 coefficient