# * if x+1 and x+2 are the factors of ax3 + bx2 +17 +10 find a and b * if x2 - 3x + 2 is a factor of x3 - x2 - px +q ,find pand q * find the value of a and b so that the x3 -ax2 - 13x + b has x-1 and x+3 as factor

1
by saluja2001

2015-04-15T07:25:00+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
1)
x+1 and x+2 are factors of  P(x) =  a x³ +  b x² + 17 x + 10
P(-1) = - a + b - 17 + 10 = 0            => a + b = 7
P(-2) = -8 a + 4 b - 34 + 10 = 0        =>  b - 2 a = 6
subtract one from the second,  a = 1/3      b = 20/3
2)
x² - 3 x + 2 = (x - 2) (x -1)  are factors of  P(x) = x³ - x² - p x + q
so P(2) = 0 = 8 - 4 - 2 p + q    =>  2p - q = 4
P(1) =    0    =  1 - 1 - p + q      =>  p = q
solving them,  q = p = 4
=====================
3
P(x) =   x³ - a x² - 13 x  + b    has  x - 1 and x+3  as the factors.
P(1) = 0  = 1 - a - 13 + b      =>    - a + b = 12
P(-3) = 0  =  -27 - 9 a + 39 + b      =>  b - 9 a = -12

solving them,  we get  a = a = 3    b = 15