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If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2?
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-...
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-...
Explanation:
Let p(x) be a quadratic polynomial, then the general form of the quadratic polynomial is:
p(x) = ax^2 + bx + c
where a, b, and c are the coefficients of the polynomial.
Now, let alpha and beta be the roots of the given quadratic polynomial, then we have:
p(alpha) = 0 and p(beta) = 0
Using the factor theorem, we can write:
p(x) = (x - alpha)(x - beta)
Expanding the above expression, we get:
p(x) = x^2 - (alpha + beta)x + alpha * beta
Comparing the coefficients of the above equation with the given quadratic polynomial, we get:
a = 1, b = -(alpha + beta), and c = alpha * beta
Solution:
Given quadratic polynomial is:
p(x) = x^2 - (k * 6) * 2(2k - 1)
On comparing the coefficients, we get:
a = 1, b = -(alpha + beta) = (k * 6) * 2(2k - 1), and c = alpha * beta = 0.5(alpha + beta)
As alpha + beta = 2c, we get:
alpha + beta = 2 * 0.5(alpha + beta)
alpha + beta = alpha * beta
Substituting the value of b, we get:
(k * 6) * 2(2k - 1) = -(alpha + beta)
(k * 6) * 2(2k - 1) = -alpha - beta
Solving the above equation, we get:
k = 0 or k = 5/6
Therefore, the value of k is either 0 or 5/6.
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2?
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If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2?.
If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of the quadratic polynomial p(x)=x^2-(k+ 6)+2(2k-1),then find the value of k if alpha plus beta is equal to alpha ×beta by 2?.
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