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If x3 -5x2 - px +24 = (x-4).q(x), then what is the value of p? |
| Answer» <html><body><p><strong>Answer</strong></p><p><strong></strong></p><p><strong>Step-by-step explanation:</strong></p><p>remainder theorem:</p><p><a href="https://interviewquestions.tuteehub.com/tag/dividend-957360" style="font-weight:bold;" target="_blank" title="Click to know more about DIVIDEND">DIVIDEND</a> =divisors <a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a> <a href="https://interviewquestions.tuteehub.com/tag/quotient-1175234" style="font-weight:bold;" target="_blank" title="Click to know more about QUOTIENT">QUOTIENT</a> + remainder</p><p></p><p>therefore, let f (X)=x^3 +(kx +8)x + k</p><p> =x^3 + kx x^2+8x+k</p><p></p><p>Dividing if(X) by x+1 gives remainder as R 1</p><p></p><p>therefore f(-1)=R 1</p><p></p><p>also ,f(2) =R 2</p><p>therefore f(-1)=(-1)^3+k(_1) ^2+8(-1)+ k</p><p></p><p> =-1 +k-8+k</p><p> =2k-9= R 1</p><p></p><p>f(2)=(2)^3 + k(2) ^3 +8 X 2 + k</p><p> =8+4K+ <a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a> +K</p><p> =5k + 24 =R 2</p><p>also, sum of remainders=R1+R1=1</p><p>therefore,(2k-9)+(5k+ 24) = 1</p><p> <a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a> k+ 15 =1</p><p> 7k=-14</p><p> k =-2</p><p></p><p>hope u have been understood</p><p>mark me as brainlist</p><p></p><p>thanku </p><p></p><p></p></body></html> | |