Question

Question 15.
Find the zeroes of the quadratic polynomial 3x2 – 75 and verify the relationship between the zeroes and the coefficients.​

Answer 1

The relationship between the zeroes and the coefficients of 3x² - 75 is verified. Refer the attachment for detailed answers. Thank you!

Answer 2

Answer:

The relationship between zeros and coefficients is verified.

Step-by-step explanation:

★ Factorize the given polynomial:

$\rightarrow$ 3x² – 75

$\rightarrow$ 3(x² – 25)

$\rightarrow$ 3(x – 5)(x + 5)

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

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★ Verifying the relationship:

In the polynomial 3x² – 75,

• a = 3
• b = 0
• c = –75

Let $\alpha$ and $\beta$ be the zeros.

• Sum of zeros :

$\rightarrow$ 5 + (–5)

$\rightarrow$ 0

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

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

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

Sum of zeros = 0

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• Product of zeros :

$\rightarrow$ 5 × –5

$\rightarrow$ –25

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$\sf{\rightarrow} \: \alpha \times \beta = \dfrac{c}{a}$

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

$\sf{\rightarrow} \: \alpha \times \beta = - 25$

Product of zeros = –25

Hence, the relationship between zeros and coefficients is verified.