Question

Find the zeroes of the quadratic polynomial 2xsquare - 9x + 4 and verify the relationship between zeros and the co-efficient.

Answer 1

zeros are 1/2,4 sum of zeros is 9/2 and product is 2 . relation between coefficients is -b/ a=9/2,c/a=2

Answer 2

Given :-

• p(x) = 2x² - 9x + 4

To Find :-

• The zeroes of the quadratic polynomial p(x).
• Verify the relationship between the zeroes and the coefficients.

Solution :-

Given,

⇒ p(x) = 2x² - 9x + 4

⇒ 2x² - 8x - 1x + 4 = 0

⇒ 2x(x - 4) -1(x - 4) = 0

⇒ (x - 4)(2x - 1) = 0

⇒ x = 4 or x = 1/2

⇒ ɑ = 4, β = 1/2

Therefore, zeroes of the given quadratic polynomial, p(x) are 4 & 1/2

Now,

ɑ + β = 4 + 1/2 = 9/2

and,

ɑ + β = -b/a = 9/2

Also,

ɑβ = 4 × 1/2 = 2

and,

ɑβ = c/a = 2

Hence, verified.