Question

If a,b are zeroes of polynomial x^2-5x+k and a^2+b^2=15then value of 15

Answer 1

Answer:

The answer is $k$ is 5

Step-by-step explanation:

 Given $a,b$ are zeroes of $x^2-5x+k=0$

   $\Rightarrow a+b=5, ab=k$, using sum and product of the zeroes concept

Now using  $(a+b)^2=a^2+b^2+2ab$

                  $\Rightarrow (5)^2=15+2k\\\Rightarrow 25=15+2k\\\Rightarrow 2k=25-15=10\\\Rightarrow k=\frac{10}{2}=5$

Answer 2

Answer:

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If α and β are the two zeros of the polynomial 25p

2

−15p+2, find a quadratic polynomial whose zeros are

2α

1

and

2β

1

.

A

8

1

(6p

2

+25p−30)

B

8

1

(6p

2

−30p+25)

C

8

1

(8p

2

+30p−25)

D

8

1

(8p

2

−30p+25)

Medium

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Solution

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Correct option is

D

8

1

(8p

2

−30p+25)

We have,

Polynomial 25p

2

−15p+2

On comparing that,

Ap

2

+Bp+C

Then,

A=25,B=−15,C=2

Given that,

Sum of roots

=α+β=

A

−B

α+β=

25

15

α+β=

5

3

Product of roots

α.β=

A

C

α.β=

25

2

Now,

2α

1

and

2β

1

Then,

Sum of roots

2α

1

+

2β

1

=

4αβ

2α+2β

=2

4αβ

(α+β)

=

2αβ

(α+β)

=

25

2×2

5

3

=

5

3

×

4

25

=

4

15

2α

1

+

2β

1

=

4

15

Product of roots

=

2α

1

×

2β

1

=

4αβ

1

=

25

4×2

1

=

8

25

So, the equation of polynomial is

p

2

⇒p 2/4

15 p+ 825

⇒ 88p 2 −30p+25

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