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If x - 3x + 2 is a factor of x - ax² + b = 0 then find the value of a and b respectively |
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Answer» Let P(x) = x3 + AX2 + bx +6 (x-2) is a factor of the polynomial x3 + ax2 + b x +6p(2) = 0 p(2) = 23 + a.22 + b.2 +6 =8+4a+2b+6 =14+ 4a+ 2b = 07 +2 a +b = 0b = - 7 -2a -(i) x3 + ax2 + bx +6 when divided by (x-3) LEAVES remainder 3.p(3) = 3 p(3) = 33 + a.32 + b.3 +6= 27+9a +3b +6 =33+9a+3b = 311+3a +b =1 => 3a+b =-10 => b= -10-3a -(ii) Equating the value of b from (ii) and (i) , we have (- 7 -2a) = (-10 - 3a)a = -3 Substituting a = -3 in (i), we getb = - 7 -2(-3) = -7 + 6 = -1Thus the values of a and b are -3 and -1 respectively. |
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