Question

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Answer 1

4. 5+√2 and 5-√2

Sum of the zeroes=5+√2+5-√2

Sum of the zeroes=10

Product of zeroes=(5+√2)(5-√2)

Product of zeroes=25-2=23

We know that quadratic polynomial is in the form of,

=k{x²-(sum of zeroes)x+product of zeroes}

By putting required values we get,

=k{x²-10x+23}

=x²-10x+23

Hence x²-10x+23 is the required polynomial.

5.

4 +√5)/(4 -√5)  + (4 -√5)/(4 +√5)

now dividing and multiplying the first term by (4 +√5) and second term by (4 -√5)

, we get,

(4 +√5)×(4 +√5)/(4 -√5)×(4 +√5) + (4 -√5)×(4 -√5)/(4 +√5)×(4 -√5)

⇒(4 +√5)²/(16 -5) +  (4 -√5)²/(16 -5)  

( applying (a² -b²)

= (a+b)(a -b))

⇒(16 +5 +8√5 +16 +5 - 8√5)/11

⇒42/11

Answer 2

Answer:

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