Question

find the zeros of the quadratic polynomial 6xsquare-3-7x and verify the relationship between the zeroes and the coefficient of the polynomial

Answer 1

The given equation is not in standard form so first we will convert it into standard form

p(x)=6x^2-7x-3

By middle term splitting

(6x^2-9x)+2x-3=0

3x(2x-3)+1(2x-3)=0

(3x+1)(2x-3)=0

x=-1/3,3/2 are the zeroes

Let alpha is equal to -1/3 and beta is equal to 3/2

Sum of zeroes =-b/a

-1/3+3/2=-(-7)/6

Taking 6 as LCM

(-2+9)/6=7/6

7/6=7/6

Product of zeroes=c/a

-1/3*3/2=-3/6

-1/2=-1/2

Hence proved

Answer 2

Question :- 6x²-7x-3

=6x²+2x-9x-3

=2x(3x+1)-3(3x+1)

=(2x-3)(3x+1) = Zeroes !!

⇒2x-3=0

or

⇒3x+1=0

⇒x=3/2 ------(1)

or

⇒ x= - 1/3 ------(2)

Verification :-

α=3/2 ,β= - 1/3

✌α+β= -b/a

⇒3/2+(-1/3)= - (-3)/6

⇒3/2-1/3=1/2

⇒7/6 =1/2

✌ αβ=c/a

⇒ 3/2(-1/3)= -7/6

⇒-1/2= -7/6

⇒1/2=7/6

_______ Hope it helps you ______