Question

1 If the equation 2x2+kx-5=0 and x2-3x-4=0 have one root in common, the find the value of K.
2 If a, ß are zeroes of x2-3x + 1= 0 the find the value of a2014+b2014+b2016 / a2015+b2015
3 If x be real, find the maximum value of 7+10x-5x2
4 If a,b,y are the roots of the equation x3-3x+11=0 then find the equation whose roots are (a+b) ,(b+y) and (y+a)
5 find the value of k for which the inequality x2-2(4k-1) x+15k2-2k-7>0 is valid for any x​

Answer 1

1 If the equation 2x2+kx-5=0 and x2-3x-4=0 have one root in common, the find the value of K.

2 If a, ß are zeroes of x2-3x + 1= 0 the find the value of a2014+b2014+b2016 / a2015+b2015

3 If x be real, find the maximum value of 7+10x-5x2

4 If a,b,y are the roots of the equation x3-3x+11=0 then find the equation whose roots are (a+b) ,(b+y) and (y+a)

5 find the value of k for which the inequality x2-2(4k-1) x+15k2-2k-7>0 is valid for any x