one zero of a quadratic polynomial is √3 and the product of the two zeroes is -5√3. Find the quadratic polynomial
Answers
The required quadratic equation of the polynomial is x²− (√3 - 5)x + (-5(√3)) = 0
Given:
One zero of a quadratic polynomial is √3 and the product of the two zeroes is -5√3.
To find:
Find the quadratic polynomial
Solution:
From the data,
One zero of a quadratic polynomial is √3
Let 'a' be the other zero of the polynomial
Given the product of zeros = -5√3
=> √3(a) = - 5√3
=> a = - 5
Hence, the two zeros of a polynomial are √3 and - 5
The equation of the polynomial will be
=> x²− (sum of zeros )x + (product of zeros) = 0
=> x²− (√3 - 5)x + (-5(√3)) = 0
=> x²− √3x + 5x - 5√3 = 0
Therefore,
The required quadratic equation of the polynomial is x²− (√3 - 5)x + (-5(√3)) = 0
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Correct question.
If one zero of a quadratic polynomial is √3 and the sum of the two zeroes is -5√3. Find a quadratic polynomial.
EXPLANATION.
One zeroes of the quadratic polynomial be √3.
The product of the two zeroes is - 5√3.
As we know that,
Concepts :
α and β are the zeroes of the quadratic polynomial.
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = -b/a.
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
Formula for quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Using this concepts in this question, we get.
One zeroes is √3.
Let us assume that,
Other zeroes will be "α".
The product of the two zeroes is - 5√3.
⇒ √3 x α = - 5√3.
⇒ α = - 5.
Other zeroes of the quadratic polynomial is α = - 5.
Formula of quadratic polynomial when √3 and - 5 are the roots of the quadratic equation.
⇒ x² - (√3 - 5)x + (√3)(-5).
⇒ x² - (√3 - 5)x - 5√3.
∴ The quadratic polynomial whose roots are √3 and - 5 is x² - (√3 - 5)x - 5√3.