Question

Find the values of 'a' and 'b' ,if 2 and 3 are the zeroes of x3+ax2+bx-30. Please answer step by step

Answer 1

$Heya$‼


Given that, 2 and 3 are the zeroes of $x^3+ax^2+bx-30$.


$p(x)=x^3+ax^2+bx-30$

Now,
$p(2)=(2)^3+a(2)^2+b(2)-30$

$=8+4a+2b-30$

$=4a+2b-22$

$=2a+b-11$

$2a+b=11$ ...(1)



And
$p(3)=(3)^3+a(3)^2+b(3)-30$

$=27+9a+3b-30$

$=9a+3b-3$

$=3a+b-1$

$3a+b=1$ ...(2)



Since 2 and 3 are zeroes of given polynomial.


So, subtracting (1) and (2)

$2a+b=11$
$3a+b=1$
_________
$-a=10$
$a=-10$


Substituting $a=-10$ in (1),
$2(-10)+b=11$
$-20+b=11$
$b=11+20$
$b=31$

Therefore,the value of a and b are –10 and 31 respectively.

Answer 2

Answer:

Step-by-step explanation:

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