Question

if f(x)=2x^3+mx^2-13x+n and 2 and 3 are roots of the equations f(x)=0, then values of m and n are- (a) 5,30 (b) -5,30 (c) -5,-30 (d) 5,-30

Answer 1

Hello!

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To find 'm' and 'n' , we will put the values of zeroes of the equation in the place of 'x' and then equate the equation to zero.

=> 2 and 3 are the zeroes of the given equation f(x) = 2x^3 + mx² - 13x + n


CASE 1

f(2) = 2(2)^3 + m(2)² - 13(2) + n = 0

= 16 + 4m - 26 + n = 0

= 4m + n = 10 (equation 1)



CASE 2

f(3) = 2(3)^3 + m(3)² - 13(3) + n = 0

= 54 + 9m - 39 + n = 0

= 9m + n = -15 ( equation 2)


Using equation 1 and equation 2

=> 4m + n = 10
9m + n = -15
(-) (-) (+)
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-5m = 25
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m = 25/ -5

m = -5


Putting value of m in equation 1

=> 4m + n = 10

= 4(-5) + n = 10

= -20 + n = 10

= n = 30


Therefore, m = -5 and n = 30.


Therefore, the answer is (b) -5,30



I hope it helped.

Thank You!

Answer 2

Answer:

see the attachment...