Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- Let f(x) = ax^ 2 + bx + c be such that f(1) = 3, f(−2) = and f(3) = 4. If f(0) + f(1) + f(−2) + f(3) = 14, then is equal to
- For p, q R, consider the real valued function f(x) = (x - p)^ 2 - q, x R and q > 0. Let a_ 1 , a_ 2 , a_ 3 and a_ 4 be in an...
- Let f(x) be a quadratic polynomial such that f(−2) + f(3) = 0. If one of the roots of f(x) = 0 is −1, then the sum of the roots...
- Let , ( > ) be the roots of the quadratic equation x^ 2 - x - 4 = 0. If P_ n = ^ n - ^ n , n N, then (P_ 15 P_ 16 - P_ 14 P_ 16 -...
- The equation px^2+qx+r=0 (where p, q, r, all are positive) has distinct real roots a and b. Which one of the following is correct?
- If the roots of the equation x^2+px+q=0 are 19^ and 26^ , then which one of the following is correct?
- The number of real roots for the equation x^2+9|x|+20=0 is
- Let m and n be the numbers of real roots of the quadratic equations x^2-12x+[x]+31=0 and x^2-5|x+2|-4=0 respectively, where [x]...
- Let , , be the three roots of the equation x^3+bx+c=0. If = 1 = – , then b^3+2c^3-3 ^3-6 ^3-8 ^3 is equal to
- The number of elements in the set n Z:|n^2-10n+19|<6 is _________
- Let the probability of getting head for a biased coin be 1/4 . It is tossed repeatedly until a head appears. Let N be the number...
- If a and b are the roots of the equation x^2-7x-1=0, then the value of a^ 21 +b^ 21 +a^ 17 +b^ 17 a^ 19 +b^ 19 is equal to...
- Let , be the roots of the quadratic equation x^2+ 6x+3=0. The ^ 23 + ^ 23 + ^ 14 + ^ 14 ^ 15 + ^ 15 + ^ 10 + ^ 10 is equal to
- Let , be the roots of the equation x^2- 2x+2=0. Then ^ 14 + ^ 14 is equal to :
- The number of real solutions of the equation 3 (x^2+ 1 x^2 )-2 (x+ 1 x )+5=0, is
- Let a R and let , be the roots of the equation x^2+60^ 1/4 x+a=0. If ^4+ ^4=-30, then the product of all possible values of a is...
- Let s = : _2(9^ 2 -4 +13)- _2 ( 5 2 .3^ 2 -4 +1 )=2 . Then the maximum value of for which the equation x^2-2 ( _ S )^2x+ _ S (...
- The set of all values of for which the equation ^22x-2 ^4x-2 ^2x= has a real solution x, is
- Let _1, _2,..., _7 be the roots of the equation x^7+3x^5-13x^3-15x=0 and | _1| | _2| | _7|. Then _1 _2- _3 _4+ _5 _6 is equal to...
- Let 0 be a real number. Let , be the roots of the equation 14x^2-31x+3 =0 and , be the roots of the equation 35x^2-53x+4 =0. Then...
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