This is the basic and exam oriented question from polynomials in which we have given a equation x²+7x+12=0 and we have to find the zeroes of the quadratic polynomials and also asked to verify the relationship between the zeroes and the coefficients

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 2A, question no 1

## Let f(x)=x²+7x+12

f(x)=x²+4x+3x+12

f(x)=x(x+4)+3(x+4)

f(X)=(x+4)(x+3)

To find the zeros , Let f(x)=0 , then

either (x+4)=0 or (x+3)=0

x=−4 or x=−3

again

sum of zeros =(−4−3)=−7=−7/1=−b/a=(-coefficient icient of x)/(−coefficient of x)product of zeros =−4×−3=12=112=ac=coefficient of x2constant term