Question

Find the zeroes of following quadratic polynomials and verify the relationship between the zeroes and the co-effecients ` 4x^(2)-x-5​​

Answer 1

Answer: zeroes are 5/4 and -1

Step-by-step explanation:

see the pic

Answer 2

Given :

• A quadratic polynomial 4x² - x - 5

To Find :

• Zeroes of the polynomial and verify the relationship between the zeroes and the coefficients .

Solution :

$\longmapsto \tt \bf{{4x}^{2} \: - x - 5 = 0 }$

By Splitting Middle Term :

$\longmapsto \tt{{4x} ^{2} - (5x - 4x) + 5 = 0}$

$\longmapsto \tt{{4x ^{2} - 5x + 4x + 5 = 0 }}$

$\longmapsto \tt{{x (4x- 5) + 1(4x - 5 )= 0 }}$

$\longmapsto \tt{(4x - 5) \: \: (x + 32) = 0}$

x = 5/4x = -1

So , 5/4 and -1 are the zeroes of Quadratic Polynomial 4x²-x-5 .

Here :

• a = 4b = -1c = -5

Sum of Zeroes :

$\longmapsto \tt {\alpha + \beta = \dfrac{ - b}{a} }$

$\longmapsto \tt \dfrac{5}{4} + ( - 1) = \dfrac{ - 1}{4}$

5/4 + (-1) = -(-1)/4

5 - 4 / 4 = 1/4

1 / 4 = 1/4

Product of Zeroes :

• ab = c/a

• 5/4 × (-1) = -5/4

• -5/4 = -5/4

HENCE VERIFIED

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