Question

Find the zeroes of the polynomial,
P(x) = 2x2 – 5 and verify the relationship
between the zeroes and their coefficient.

Answer 1

Given :- Find the zeroes of the polynomial, P(x) = 2x² – 5x - 12 = 0 and verify the relationship between the zeroes and their coefficient. ?

Answer :-

→ 2x² - 5x - 12 = 0

→ 2x² -8x + 3x - 12 = 0

→ 2x(x - 4) + 3(x - 4) = 0

→ (2x + 3)(x - 4) = 0

putting both equal to zero we get,

→ x = (-3/2) and 4 .

Now, First Relation is :-

→ Sum of Zeros = - (coefficient of x) /(coefficient of x²)

Putting both values ,

→ (-3/2) + 4 = -(-5)/2

→ (-3 + 8)/2 = (5/2)

→ (5/2) = (5/2) ( Hence Verified. )

Second Relation :-

→ Product Of Zeros = Constant Term / (coefficient of x²)

Putting both Values ,

→ (-3/2) * (4 = (-12) / (2)

→ (-6) = (-6) ( Hence Verified. )

Learn more :-

JEE mains Question :-

https://brainly.in/question/22246812

. Find all the zeroes of the polynomial x4

– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

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