Frequent Quadratic Equations Logarithm Questions

If a, b, c are the sides of triangle ABC satisfying log(1+c/a) + log a – log b = log 2. Also a(1 – x2) + 2bx + c(1 + x2) = 0 has two equal roots. Find the value of sin A + sin B + sin C. ...

The equation x + frac{2}{{1 - x}} = 1 + frac{2}{{1 - x}}, has a) No real root b) One real root c) Two equal roots d) Infinitely many roots ...

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Find the square root of ((0.75)^3/1-(0.75)) + (0.75 + (0.75)^2 + 1). My problem is that I am getting an answer 2.5 which is NOT one of the options provided. ...

\sqrt{x+\sqrt{x+\sqrt{x+}..}}=y \sqrt{y+\sqrt{y+\sqrt{y+}..}}=5 find √(x+y) ...

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The solution of the equation {log _7}{log _5}(sqrt {{x^2} + 5 + x} ) = 0 a) x = 2 b) x = 3 c) x = 4 d) x = - 2 ...

The value of sqrt {(log _{0.5}^24)} is a) –2 b) sqrt {( - 4)} c) 2 d) None of these ...

If {log _{10}}2 = 0.30103,{log _{10}}3 = 0.47712, the number of digits in {3^{12}} imes {2^8} is a) 7 b) 8 c) 9 d) 10 ...

If one root of the equation ax2+bx+c=0 is the square of the other, then a(c-b)3=cX, where X is (a) a3+b3 (b) (a-b)3 (c) a3-b3 (d) N.O.T Please show the method .. ...

Σ 1/1+xa-b+xa-c =? (A) 1 (B)-1 (C) 0 (D) N.O.T. ...

If the roots of the equation x2-bx/ax-c = m-1/m+1 are equal but opposite in sign, then the value of of m will be (a) a-b/a+b (b) b-a/a+b (c) a+b/a-b (d) a+b/b-a Brahmastra, Quadratic Equations Q No. 10. ...

The solution of the equation 2{x^2} + 3x - 9 le 0 is given by a) frac{3}{2} le x le 3 b) - 3 le x le frac{3}{2} c) - 3 le x le 3 d) frac{3}{2} le x le 2 ...

If the sum of the roots of the equation 2333x-2+2111x+1=2222x+2+1 is expressed in the form a/b find a + b, where a/b is in its lowest form. ...

The solution set of frac{{{x^2} - 3x + 4}}{{x + 1}} > 1,,x in R , is a) (3,,, + infty ) b) ( - 1,,,1) cup (3,,, + infty ) c) [ - 1,,,1] cup [3,,, + infty ) d) None of these ...

If the equation ax3+3bx2+3cx+d=0 has two equal roots,show that it must be equal to bc-ad/2(ac-b2) . ...

If each pair of the following three equations x2+ax+b=0, x2+cx+d=0, x2+ex+f=0 has exactly one root in common,then show that (a+c+e)2=4(ac+ce+ea-b-d-f). ...

\hspace{-16}$Find all real polynomials $\bf{p(x)}$ such that $\bf{p(x)\cdot p(x+1)=p(x^2)\;\forall x\in \mathbb{Z}}$ ...

\hspace{-16}$Solution for real $\bf{\left(a\;,b\;,c\right)}$ in \\\\ $\bf{[a]+c\{c\}-b\{b\}=0.16}$\\\\ $\bf{b+a\{a\}-c\{c\} = 0.25}$\\\\ $\bf{c[c]+b\{b\}-a\{a\} = 0.49}$\\\\ Where $\bf{[x] =}$ Integer part of $\bf{x}$\\\\ and ...

If p(x) is an 11th degree polynomial such that p(x) = 1/1+x for x = 1, 2, 3,...11, then find p(12). ...

left[ {frac{1}{4}} ight] + left[ {frac{1}{4} + frac{1}{{200}}} ight] + left[ {frac{1}{4} + frac{1}{{100}}} ight] + .....left[ {frac{1}{4} + frac{{199}}{{200}}} ight] is ...

The roots of the equation {7^{{{log }_7}}}^{({x^2} - 4x + 5)} = x - 1 are ...

If {a^x} = bc,{b^y} = ca,,{c^z} = ab, then xyz = ...

If {9^x} - 4 imes {3^{x + 2}} + {3^5} = 0, then the solution pair is ...

If x = sqrt {7 + 4sqrt 3 } , then x + frac{1}{x} = ...

If {log _{12}}27 = a, then {log _6}16 = ...

The set of values of x which satisfy 5x + 2 < 3x + 8 and frac{{x + 2}}{{x - 1}} < 4 , is ...