Mathematics questions
18011 published questions with worked solutions.
- If the product of the roots of ax^2+bx+c=0 is 9 and a,b,c are in A.P., then find the sum of its roots.
- If and are the roots of the equation x^2-a(x+1)-b=0, then find the value of ^2+2 +1 ^2+2 +b + ^2+2 +1 ^2+2 +b .
- Let a,b 1,2,3,4,5 . Find the number of equations of the form ax^2+bx+1=0 having real roots.
- If and are the roots of the equation 6x^2+11x+3=0, then find the value of (6 +11)^2+(6 +11)^2.
- If the roots of the equation x^2+ 3ax-b=0 are 15^ and 45^ , then find the value of 7+a+b.
- If r and s are the roots of the equation x^2-10px-11q=0 and p and q are the roots of the equation x^2-10rx-11s=0, then find the...
- Let f(x)=ax^2+bx+c, where a,b,c are real constants and a 0. If f(13)=-8f(3) and f(-7)=0, then find the value of f(5).
- If and are the roots of the equation x^2-4x-1=0, find ^5+ ^5.
- Let and be the roots of the equation x^2+x+1=0. If the equation whose roots are ^ 58 and ^ 19 is ax^2+bx+c=0, then find the value...
- If and are the roots of x^2-5x+16=0 and ^2+ ^2, 2 are the roots of x^2+ax+b=0, then find the value of a+b.
- Find the product of the roots of the equation 4^x-3 (2^ x+3 )+128=0.
- Find the smallest prime number x such that it satisfies 2^ _ 2 (x-1) >x+5.
- If one of the roots of the equation 6x^2+kx+6=0, k>0, is square of the other, then find the value of k.
- If and are the roots of x^2-5x+4=0, then find the value of ^3 2 cosec ^2 ( 12 ^ -1 )+ ^3 2 ^2 ( 12 ^ -1 ).
- Find the value of such that the sum of the squares of the roots of x^2+(4- )x+3= has the least value.
- If the roots of the equation 12x^2+mx+5=0 are in the ratio 3:2, then find the value of m^2.
- If the roots of the quadratic equation x^2-6x+ _2 =0 are real, then find the maximum value of .
- Find the largest integral value of m for which the quadratic expression y=x^2+(2m+4)x+7m+8 is positive for all x R.
- If one of the roots of the equation px^2-6x+q=0, where p and q are real numbers, is 32+ 72i, then find the value of |p-q|.
- Let z be a complex number satisfying the equation 2|z-1|+i+z=0. Find the number of such complex numbers.