Question

Content quality needed

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1. If one solution of the equation 3x^2 -8x+2k +1 is seven times the other . Find the solutions and the value of K .

2. For what value of K to the zeros of polynomial x^2 -5x+k are differ by 1

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Answer 1

(1)

Given f(x) = 3x^2 - 8x + 2k + 1.

On comparing with ax^2 + bx + c + d, we get

we get a = 3, b = -8, c = 2k + 1

Now,

Let one of the zero be a.

Given that one of the zeroes is seven times the other. = > 7a.

= > we know that sum of zeroes = -b/a

a + 7a = -8/3

8a = 8/3

a = 1/3  ----- (1)


Therefore the other zero is 7a = 7(1/3)

                                                   = 7/3.


= > Also, the product of zeroes  = c/a

a * 7a = 2k + 1 /3

1/3 * 7/3 = 2k + 1/3

7/9 = 2k + 1/(3)

2k + 1 = 7/3

2k = 7/3 - 1

2k = 4/3

k = 2/3.


(2) 

Let a, b be the zeroes of the polynomial x^2 - 5x + k.

On comparing with ax^2 + bx + c, we get

a = 1, b = -5, c = k.

We know that sum = -b/a

= > a + b = 5/1

= > a + b = 5   ------ (1)


We know that product = c/a

= > ab = k/1

= > ab = k.  ------ (2)


Now,

Given that they differ by 1.

= > a - b = 1.  ------ (3)

On solving (1) & (3), we get

a + b = 5

a - b = 1

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2b = 6

b = 3.

Substitute b = 6 in (1), we get

= > a + b = 5

= > a + 3 = 5

= > a = 2.


Substitute a = 2, b = 3 in  (2), we get

= > 2 * 3 = k

k = 6.


Therefore the value of k = 6.


Hope this helps!

Answer 2

Heya....frst answer is dis....
Hope helps...

@skb