(i)  If one of the zeroes of the polynomial 3x2 – 8x + 2k + 1 is seven times the other, find the zeroes and the value of k.

 

(ii)  If m, n are zeroes of ax2 – 5x + c, find the value of a and c if m + n = m.n = 10

 

(iii)  Find the zero of the polynomial 3x3 – 5x2 + 2

Asked by gpnkumar0 | 11th May, 2017, 07:24: AM

Expert Answer:

begin mathsize 16px style Given space polynomial space is space 3 straight x squared minus 8 straight x plus left parenthesis 2 straight k plus 1 right parenthesis
Let space one space of space the space zero space be space straight alpha.
Then comma space other space zero equals 7 straight alpha
Now comma space sum space of space zeros comma
straight alpha plus 7 straight alpha equals negative fraction numerator left parenthesis negative 8 right parenthesis over denominator 3 end fraction
rightwards double arrow 8 straight alpha equals 8 over 3
rightwards double arrow straight alpha equals 1 third
Product space of space zeros comma
straight alpha cross times 7 straight alpha equals fraction numerator 2 straight k plus 1 over denominator 3 end fraction
rightwards double arrow 7 straight alpha squared equals fraction numerator 2 straight k plus 1 over denominator 3 end fraction
rightwards double arrow 21 cross times 1 over 9 equals 2 straight k plus 1
rightwards double arrow 7 over 3 equals 2 straight k plus 1
rightwards double arrow 2 straight k equals 7 over 3 minus 1 equals 4 over 3
rightwards double arrow straight k equals 2 over 3
Note colon space Please space post space one space query space at space straight a space time.
end style

Answered by Rashmi Khot | 11th May, 2017, 04:29: PM