find the zeroes of each of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients. 1. 3x² - x - 4
Answers
Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(vi)3x² – x – 4
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(vi)3x² – x – 4
(vi) 3x² – x – 4
Factorize the equation
3x² – x – 4
Compare the equation with ax² + bx + c = 0
We get
a = 3 ,b=-1 c= -4
to factorize the value we have to find two value which
sum is equal to b =-1
product is a*c = 3*-4 = -12
3 and -4 are such number which
Sum is 3 – 4 = - 1
Product is 3 *- 4 = - 12
So we can write middle term -x = 3x – 4x
We get
3x² + 3x - 4x - 4 = 0
3x(x +1) -4(x + 1) = 0
(x + 1) (3x - 4) = 0
x + 1 = 0 , 3x - 4 = 0
Solve for first zero
x = - 1
solve for second zero
3x-4 = 0
3x = 4
x = 4/3
Sum of zeros -b/a = -(-1/3) = 1/3
Product of zero c/a = -4/3 = 4/3