find the sum and product of the zeroes of the polynomial px2-qx+pq
Answers
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➡Sum of zeroes = -B / A
Sum of zeroes = q / p
➡Product of Zeroes = C / A
Product Of zeores = pq / p
Product of Zeroes = q
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Concept:
Suppose a quadratic polynomial is given by,
f(x) = ax² + bx + c
The zeros of the above polynomial mean the values of x for which the polynomial is equal to zero.
f(x) = 0
ax² + bx + c = 0
Let the zeros be α and β.
Sum of zeros, α + β = -Coefficient of x/Coefficient of x²
= -b/a
Product of zeros, αβ = Independent term/Coefficient of x²
= c/a
Given:
The given polynomial is,
f(x) = px² - qx + pq
Find:
The sum and product of the zeroes of the polynomial.
Answer:
The sum of zeros of the given polynomial is q/p.
The product of zeros of the polynomial is q.
Solution:
Let the zeros of the polynomial be α and β.
The given polynomial is px² - qx + pq.
Coefficient of x², a = p
Coefficient of x, b = -q
Independent term, c = pq
Sum of zeros, α+β = -b/a
= -(-q)/p
= q/p
Product of zeros, αβ = c/a
= pq/p
= q
Hence, α+β = q/p and αβ = q.
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