Question

Find the zeroes of the quadratic polynomial 3x2

– 75 and verify the relationship between

the zeroes and the coefficients​

Answer 1

Step-by-step explanation:

Find the zeroes of the quadratic polynomial 3x2

– 75 and verify the relationship between

the zeroes and the coefficients

Answer 2

Answer:

The relationship between zeros and coefficients is verified.

Step-by-step explanation:

★ Factorize the given polynomial:

→ 3x² – 75

→ 3(x² – 25)

→ 3(x – 5)(x + 5)

So, x = 5 or x = –55, and –5 are zeros of 3x² – 75

___________________

★ Verifying the relationship:

In the polynomial 3x² – 75,

a = 3

b = 0

c = –75

$\large\sf \: Let \: \alphaα \: and \: \betaβ \: be \: the \: zeros.$

Sum of zeros :

→ 5 + (–5)

→ 0

____________________________

$\sf{\rightarrow} \: \alpha + \beta = \dfrac{ - b}{a}$

$\sf{\rightarrow} \: \alpha + \beta = \dfrac{ - 0}{3}$

$\sf{\rightarrow} \: \alpha + \beta = 0$

Sum of zeros = 0

___________________

Product of zeros :

→ 5 × –5

→ –25

____________________________

$\sf{\rightarrow} \: \alpha \times \beta = \dfrac{c}{a} \\ \\ \: \: \: \: \: \sf{\rightarrow} \: \alpha \times \beta = \dfrac{ - 75}{3} \\ \\ \: \: \: \: \sf{\rightarrow}\: \alpha \times \beta = - 25$

Product of zeros = –25

Hence, the relationship between zeros and coefficients is verified.