write one of the zeros of the polynomials 2x²-5x - 3
Answers
Answer:
one of the zeros of the polynomial is (x-3)and (x-3)
Question :
write one of the zeroes of the polynomial : 2x² - 5x - 3
Answer :
3 , -1/2 are the zeroes
Step-by-step explanation :
Given quadratic polynomial,
2x² - 5x - 3
=> It is of the form ax² + bx + c
a = 2, b = -5, c = -3
a - coefficient of x²
b - coefficient of x
c - constant term
By sum-product pattern,
>> Find the product of quadratic term [ax²] and constant term [c]
= 2x² × (-3)
= -6x²
>> find the factors of "-6x²" in pairs
=> (x) (-6x)
=> (-x) (6x)
=> (2x) (-3x)
=> (-2x) (3x)
>> From the above, find the pair that adds to get linear term [bx]
x - 6x = -5x
>> So, split -5x as -6x and x
2x² - 5x - 3 = 0
2x² - 6x + x - 3 = 0
>> Find the common factor
2x(x - 3) + 1(x - 3) = 0
(x - 3) (2x + 1) = 0
=> x - 3 = 0 ; x = +3
=> 2x + 1 = 0 ; x = -1/2
∴ 3 and -1/2 are the zeroes of the given polynomial.