find the quadratic polinomial whose
zeroes are 5-3√2 and 5+3√2
Answers
EXPLANATION.
Quadratic polynomial whose zeroes are,
⇒ 5 - 3√2, 5 + 3√2.
As we know that,
Sum of zeroes of quadratic equation.
⇒ α + β = -b/a.
⇒ 5 - 3√2 + 5 + 3√2.
⇒ 10.
Products of zeroes of quadratic equation,
⇒ αβ = c/a.
⇒ (5 - 3√2)(5 + 3√2).
⇒ [(5)² - (3√2)²].
⇒ [25 - 18].
⇒ 7.
Formula of quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (10)x + 7 = 0.
⇒ x² - 10x + 7 = 0.
MORE INFORMATION.
Nature of the factor of the quadratic expression.
(1) = Real and different, if b² - 4ac > 0.
(2) = Rational and different, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.
Answer:
k[x^2-10x+7] is the required polynomial
Step-by-step explanation:
Question:
Find the quadratic polinomial whose zeroes are (5-3√2) and (5+3√2)
GIven:
- Zeroes of the polynomial =(5-3√2) and (5+3√2)
To find:
- The quadratic polynomial
Solution:
- Let α be (5-3√2)
- Let β be (5+3√2)
Sum of zeroes:
α+β = 5-3√2+5+3√2
α+β = 10
Product of zeroes:
αβ = (5-3√2)(5+3√2)
αβ= 5^2-(3√2)^2
αβ = 25-18
αβ = 7
Therefore the polynomial is:
- k[x^2-(α+β)x+αβ]
Apply the formula:
k[x^2-10x+7]
Note: Here, k is a constant value