Question

solve the this question​

Answer 1

Step-by-step explanation:

x^2-(sum of roots)x+product of roots=0

x^2-10x+23=0

Answer 2

Step-by-step explanation:

Given:-

Given zeroes are 5+√2 and 5-√2

To find:-

Find a quadratic polynomial whose zeroes are

5+√2 and 5-√2?

Solution:-

Given zeroes are 5+√2 and 5-√2

Let α = 5+√2

and β = 5-√2

We know that

If α ,β are the zeores then the quadratic

polynomial is K[x^2-(α + β )x +αβ]

Now On Substituting the values of α ,β in the

above formula then we get

=>K[x^2-(5+√2+5-√2)x +(5+√2)(5-√2)]

=>K[x^2-(5+5)x +{(5)^2-(√2)^2}]

Since (a+b)(a-b)=a^2-b^2

Where a = 5+√2 and b=5-√2

=>K[x^2-10x+(25-2)]

=>K[x^2-10x+23]

If K= 1 then the required pilynomial is

x^2-10x+23.

Answer:-

The quadratic polynomial whose zeroes are

5+√2 and 5-√2 is x^2 -10x +23

Used formulae:-

• If α ,β are the zeores then the quadratic
• polynomial is K[x^2-(α + β )x +αβ]

• (a+b)(a-b)=a^2-b^2