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If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta?
Most Upvoted Answer
If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of ...
Solution:
Given, alpha and beta are zeros of the polynomial 2x^2 - 5x + 3.
To find: Value of 1/2alpha + 1/2beta
We know that, sum of the zeros of a quadratic polynomial ax^2 + bx + c is given by -b/a and product of the zeros is given by c/a.
i.e., alpha + beta = 5/2 and alpha x beta = 3/2.
So, 1/2alpha + 1/2beta
= (alpha + beta)/2alpha x (alpha + beta)/2beta
= [(alpha + beta)^2]/4alpha x beta
= [(5/2)^2]/4 x (3/2)
= 25/16
Therefore, the value of 1/2alpha + 1/2beta is 25/16.
Given, alpha and beta are zeros of the polynomial 2x^2 - 5x + 3.
To find: Value of 1/2alpha + 1/2beta
We know that, sum of the zeros of a quadratic polynomial ax^2 + bx + c is given by -b/a and product of the zeros is given by c/a.
i.e., alpha + beta = 5/2 and alpha x beta = 3/2.
So, 1/2alpha + 1/2beta
= (alpha + beta)/2alpha x (alpha + beta)/2beta
= [(alpha + beta)^2]/4alpha x beta
= [(5/2)^2]/4 x (3/2)
= 25/16
Therefore, the value of 1/2alpha + 1/2beta is 25/16.
Community Answer
If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of ...
Polynomial is 2x^2 - 5x - 3= 0
2x^2-6x+x-3=0
2x(x-3)+1(x-3)=0
(x-3)(2x+1)=0
x-3=0
x=3 alpha is 3
1/2alpha 1/2*3=1.5
2x+1=0
2x=-1
x=-1/2 bita is -1/2
1/2bita
1/2*-1/2=-0.25
2x^2-6x+x-3=0
2x(x-3)+1(x-3)=0
(x-3)(2x+1)=0
x-3=0
x=3 alpha is 3
1/2alpha 1/2*3=1.5
2x+1=0
2x=-1
x=-1/2 bita is -1/2
1/2bita
1/2*-1/2=-0.25
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If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta? for Class 10 2025 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 zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta?.
If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta? for Class 10 2025 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 zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are zeros of polynomial 2x^2-5x 3 find the value of 1/2alpha 1/2beta?.
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