Question

Find the zeros of the quadratic polynomial 6x
2
−3−7x and verify the relationship between the zeros and the coefficient of the polynomial​

Answer 1

SOLUTION:-

⠀⠀⠀⠀⠀$\underline{\sf{\red{Question}}}$

• Find the Zeros of the Quadratic polynomial 6x²-3-7x and verify relationship

⠀⠀⠀⠀⠀$\underline{\sf{\red{Given}}}$

• p(x) = 6x²-7x-3=0

⠀⠀⠀⠀⠀$\underline{\sf{\red{To\:Calculate}}}$

• Zeros and Verify relationship

⠀⠀⠀⠀⠀$\underline{\sf{\red{Explanation}}}$

Find Zeros

p(x) = 6x²-7x-3=0

➫ 6x²-(9-2)x-3=0

➫ 6x²-9x+2x-3=0

➫ 3x(2x-3)+1(2x-3)=0

➫ (2x-3)(3x+1)=0

➫ (2x-3)=0,(3x+1)=0

➫ 2x=3,3x=-1

➫ x=3/2,x=-1/3

${\sf{\blue{Zeros\:are ➫ 3/2,-1/3}}}$

Sum of zeros = -b/a

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

➫ 3/2-1/3 = 7/6

➫ 9-2 /6 = 7/6

${\sf{\blue{ 7/6 = 7/6}}}$

Product of zeros = c/a

3/2×(-1/3)= -3/6

${\sf{\blue{-3/6= -3/6}}}$

${\huge{\underline{\underline{\sf{\red{Hence\: Verified!!}}}}}}$

Answer 2

Given :-

• Quadratic polynomial : p(x) = 6x² - 7x - 3x = 0.

To Find :-

• Verify the relationships between zeroes and the coefficient of the quadratic polynomial.

Solution :-

First we need to find out zeroes of quadratic polynomial.

p(x) = 6x² - 7x - 3 = 0

↪ 6x² - 9x + 2x - 3 = 0

↪ 3x(2x - 3) + 1(2x - 3) = 0

↪ (2x - 3) (3x + 1) = 0

↪ x = (3/2 , -1/3)

Zeroes of quadratic polynomial = (3/2 , -1/3)

↪Sum of zeroes = -b/a

↪ 3/2 + -1/3 = -(-7/6)

↪9-2/6 = 7/6

↪7/6 = 7/6

↪Product of zeroes = c/a

↪ 3/2 × -1/3 = -3/6

↪-3/2×3 = -3/6

↪ -3/6 = -3/6

Hence, Relationship is verified!!