for the quadratic polynomial f(x) = 4x2-8ax+a, the statements which hold good is/are(multiple correct answers) give explaination a ) - Maths - Logs Equations and Inequalities

Question

for the quadratic polynomial f(x) = 4x2-8ax+a, the
statements which hold good is/are(multiple correct answers)
give explaination
a ) there is only one integral 'a' for which f(x) is non-negative
for all x belongs to R
b ) for a< 0, the number lies between the zeroes of the
polynomial
c ) f(x) =0 has two distinct solutions in (0,1) for 'a' belonging
to (1/7,4/7)
d ) the minimum value of f(x) for minimum value of 'a' for which
f(x) is non-negative for all x in R is zero

Ghanshyam Dhakar · Accepted Answer

Dear student, fx = 4x2-8ax+a D = b2-4ac = 64a2-16aD = 16a4a-1for two distinct solution D>0then a4a-1>0a∈-∞,0∪14,∞for two exact solution and non negative fx for all x in RD=0then a4a-1=0a∈0,14for no solution and positve fx for all x in RD<0then a4a-1<0a∈0,14answer d and I do not understand option b Hope this information will clear your doubts If you have any more doubts just ask here on the forum and our experts will try to help out as soon as possible Regards