Math, asked by kharatgirish, 8 months ago

Sum of zeros = a + b = -8 and product of zeros = aß = 6. Form a polynomial whose zeros are a + 2B and B + 2a

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Answered by mastermaths55

Answer:

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Answered by ronaldoChristiano

$<body bgcolor= black><font color=orange >$ If p and q are the zeroes of quadratic polynomial ax²+bx+c then evaluate p-q.

(this is the correct form of the question.)

$\color{green}{Given:}$

p and q are the zeroes of quadratic polynomial ax²+bx+c.

$\color{red}{To\:Find:}$

The value of p-q.

$\color{blue}{Solution:}$

1) If p and q are the zeros of the polynomial the there is a relation between the zeros and the coefficient of the quadratic polynomial.

2) Sum of the roots = p+q= −b/a = −(coefficient of x) / (coefficient of x²)

Product of the toots = pq = c/a = (coefficient of x) / (coefficient of x²)

3) To find p-q we have to find the square of the first expression.

(p+q)²= (−b/a)²
p² + q² + 2pq = b²/a²
p² + q² + 2pq - 4pq = b²/a² - 4pq (Subtract 4pq form both side)

p² + q² - 2pq = b²/a² - 4c/a

(p-q)² = (b² - 4ac) / a²

(p-q) = √[(b² - 4ac) / a²]

(p-q) = √(b² - 4ac) / a

The value of (p-q) = √(b² - 4ac) / a

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Sum of zeros = a + b = -8 and product of zeros = aß = 6. Form a polynomial whose zeros are a + 2B and B + 2a​

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Sum of zeros = a + b = -8 and product of zeros = aß = 6. Form a polynomial whose zeros are a + 2B and B + 2a