Question

find quadratic equation whose roots are 7±2√5



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Answer 1

Answer:

x^2 - 14x + 29          

Step-by-step explanation:

Answer 2

GIVEN :-

• Roots of a quadratic equation are 7 ± 2√5.

TO FIND :-

• The required quadratic equation.

SOLUTION :-

Here the roots of the quadratic equation are 7 - 2√5 , 7 + 2√5.

Now , As we know that,

⇒ quadratic equation = x² - (α + β)x + (α × β)

• α = 7 + 2√5
• β = 7 - 2√5

⇒ quadratic equation = x² - (7 + 2√5 + 7 - 2√5)x + (7 + 2√5)(7 - 2√5)

⇒ quadratic equation = x² - (7 + 7)x + (7)² - (2√5)²

⇒ quadratic equation = x² - 14x + 49 - 4 × √25

⇒ quadratic equation = x² - 14x + 49 - 4 × 5

⇒ quadratic equation = x² - 14x + 49 - 20

⇒ quadratic equation = x² - 14x + 29

Hence the required quadratic equation is x² - 14x + 29.