Answer : $\large\frac{-25}{12}$

Answer : $1$

Given f(x) = $x^3+4x^2+x-6$$$\alpha\beta\gamma = \frac {-d}{d} = -(\frac{-6}{1})$Ans = 6

$\text {Since} x+2$ is a factor of $x^2+ax+2b$$ P (-2) = (-2)^2 + a (-2) + 2b = 0$$ \implies { 4 - ...

$f(x)=x^3-12x^2+39x-28$Let a-d, a, a+d be the zeroes of the Polynominal$\text {Sum of Zeroes} = - (...

$f(x)=x^3-5x^2-2x+24$$ \text {Let} \; \alpha\beta = 12$$ \alpha + \beta + \gamma = - (-5) = 5$$ \alp...

Answer : $\leq1$

Let P(x) = $x^2-x-(2k+2)$$ P(-4) = (-4)^2 - (-4) - (2k + 2) = 0$$ \implies 16 + 4 - 2k - 2 = 0$$ \im...

Solution : https://clay6.com/mpaimg/a5.jpgAnswer : $a=2,b=0$Class of polynomialsIf the remainder is ...

Solution : https://clay6.com/mpaimg/ap50.jpgSince the remainder is zero $x(a+1)=0$$=> a=-1$and $b...

The given roots are 53√\sqrt{\frac{5}{3}} and - 53√\sqrt{\frac{5}{3}}The equation formed by the give

Answer : $x-2$

Answer : $-28$

Answer : $-3$

Answer : $-1$

Let a - d, a and a+d be the zero of the polynomial; $x^3-px^2+qx-r$a - d + a + a + d = -(-p) /1 = p$...

Answer : $-\large\frac{3}{2}$

Given, $5y^2-7y+1=0$$\alpha + \beta = -(\frac{-7}{5}) = \frac{7}{5}$ and $\alpha\beta = \frac{1}{5}$...

Solution : given $9x^2+8kx+16=0$Since it has equal roots$b^2-4ac=0$=> $(8k)^2 -4 \times 9 \times ...

Solution : Sum of the roots $= \alpha +\beta= \large\frac{-4}{1}$ (ie) $1+\beta +\beta=-4$$2 \beta=-...

Answer : $-\large\frac{1}{2}$

Answer : $\large\frac{-5}{16}$

Answer : $(2x-(a-b)),(2x+(a+b))$

Answer : $(ax-2b),(ax-b)$

Answer : $(x+2),(x-1)$

Solution : given $\large\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x}$=> $\large\frac{x-1 +2(x-2)}{(x-2...

Tag it a class 10 quadratic equation$ Given : \large\frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}$$\begi...

Given $x^2-8x+k=0$also $\alpha^2 + \beta^2 = 40 \implies (\alpha + \beta)^2 - 2\alpha\beta = 40$sum ...

Answer : $k=-1$ or $\large\frac{2}{3}$

$ \text {Given:} \; \alpha - \beta = 1 \implies \; \alpha = 1 + \beta$$ \text {also} \; x^2 - 5x + K...

Given $\alpha = 2\beta $ and $x^2 - 3x + k = 0$ $\begin{align*}\text{Sum of the roots} = 2 \beta + \...

Given : One root is double the other (i.e) $\beta = 2\alpha$ $ ax^2 + bx + c = 0 $ Sum of the roots ...

$4x^2+5x+\lambda=0$also $\beta = \frac{1}{\alpha}$sum of the roots is $\alpha + \frac{1}{\alpha} = \...

Given$x^2 - (k+6)x + 2(2k-1) = 0$ sum of the roots = $\frac{1}{2}$ product of rootssum of the roots ...

Answer : $m=\large\frac{-15}{2}$; second root is $\large\frac{3}{2}$

$3x^2+(2k+1)x-(k+5)=0$ a = 3, b = (2k + 1) , c = -(k + 5)Given $\implies$ Sum of the roots = Produc...

Answer : $x^2+(2-\sqrt 5)x-2\sqrt 5=0$

Polynomial $ x^2 - (\sqrt2 + 1 )x + \sqrt2 = 0$$x^2 - \sqrt2x - x + \sqrt2 = 0$$x(x - \sqrt2) - 1(x ...

quadratic equation $\large\frac{x-a}{x-b}+\frac{x-b}{x-a}=\frac{a}{b}+\frac{b}{a}$$\implies \frac{(x...

$x^2+2ab=(2a+b)x$$\implies x^2 -(2a + b)x + 2ab = 0$$\implies x^2 -2ax - bx +2ab = 0$$\implies x(x-2...

Answer : $x=-\large\frac{a}{a+b};\frac{-(a+b)}{a}$

Answer : $x=1,1$Given $x=\large\frac{1}{2-\Large\frac{1}{2-\Large\frac{1}{(2-x)}}}$(ie) $x=\large\fr...

Answer : $\large\frac{-3}{2}$

$ax^2+7x+6=0$$P(\frac{2}{3})= a(\frac{2}{3})^2 + 7(\frac{2}{3}) + b = 0$$\implies \frac{4a}{9} + \fr...

$P(2) = 2(2)^2 + k(2 - 6 = 0)$$\implies 8 + 2k - 6 = 0$$\therefore k = -1$

Answer : $k=\large\frac{15}{2},\normalsize m=9$

$x = -a^2$$\begin{align*}P(-a) = a^2 + 2a(-a) -k & = 0 \\ a^2 - 2a^2 - k & = 0 \\ \therefore...

Toolbox:equation of a circle passing through the origin is $x^2+y^2=a^2$ where $a$ is the radius.The...

Toolbox:General equation of hyperbola which lies on the $x$-axis is $\large\frac{x^2}{a^2}-\frac{y^2...

Toolbox:General equation of a hyperbola which lies on the $y$ axis is $\large\frac{x^2}{a^2}-\frac{...