CBSE Class 10 Mathematics (Demo)

The zeroes of the polynomial $$x^{2}+x(c-b)+(c-a)(a-b)$$ are

The sum of the zeroes of the polynomial $$4 x^{2}-2007$$ is

The zeroes of the polynomial $$x^{2}-2 a x+\left(a^{2}-b^{2}\right)$$ are

The sum of the zeroes of the polynmial $$(x-1)(x-2)(x-3) \ldots \ldots .(x-10)$$ is

The zeroes of the polynomial $$(a-x)^{2}+(b-x)^{2}-(a-b)^{2}$$ are

The zeroes of the polynomial $$x^{6}-9 x^{3}+8$$ are

The sum of the zeroes of the quadratic expression $$\lambda^{2}\left(x^{2}-x\right)+2 \lambda x+3$$ is

The product of thes zeroes of the quadratic polynomial $$(a+c)\left(a x^{2}+2 b x+c\right)-2\left(a c-b^{2}\right)\left(x^{2}+1\right)$$ is

If the sum of the zeroes of $$a x^{2}+b x+c$$ is equal to the sum of their squares, then

If one zero of $$x^{2}-(p-1) x+10$$ is 5 , then the value of $$\boldsymbol{p}$$ is

The product of zeroes of the expression $$x^{1997}+3 x^{1996}+\ldots \ldots \ldots \ldots . .+99 x$$ is

The zeroes of the expression $$a(a+b) x^{2}-b(a-b) x-(a-b)^{2}$$ are

If $$\mathbf{p}$$ and $$\mathbf{q}$$ are the zeroes of $$x^{2}+p x+q$$, then

The values of a and $$\mathbf{k}$$, if the zeroes of $$3 x^{2}+2 k x+k+2$$ are the reciprocals of the zeroes of $$2 a x^{2}+(k+a) x+3$$ are

The numerical difference of the zeroes of $$x^{2}-7 x-9$$ is

The value of $$\lambda$$ for which the quadratic expression $$3 x^{2}+2\left(\lambda^{2}+1\right) x+\left(\lambda^{2}-3 \lambda+2\right)$$ has zeroes of opposite signs, lies in the interval

If the ratio of the zeroes of the expression $$x^{2}+p x+q$$ is equal to the ratio of the zeroes of $$x^{2}+l x+m$$, then

If $$\alpha, \beta$$ are zeroes of the expression $$a x^{2}+b x+c$$, then the value of $$\left(1+\alpha+\alpha^{2}\right)\left(1+\beta+\beta^{2}\right)$$ is

The zeroes of $$\left(x^{2}-3 x+2\right)(x)(x-4)$$ are

If $$\alpha, \beta$$ are the zeroes of $$a x^{2}+b x+c$$, then $$\frac{\alpha}{\beta^{2}}+\frac{\beta}{\alpha^{2}}$$ is

If $$\alpha, \beta$$ are the zeroes of $$a x^{2}-2 b x+c$$, then $$\alpha^{3} \beta^{3}+\alpha^{2} \beta^{3}+\alpha^{3} \beta^{2}$$ is

If $$\alpha, \beta$$ are the zeroes of $$a x^{2}+b x+c$$, then the value of $$\left(\frac{1}{\alpha^{2}}-\frac{1}{\beta^{2}}\right)^{2}$$ is

If $$\alpha, \beta$$ are the zeroes of $$a x^{2}+b x+c$$, then the value of $$\frac{\alpha-1}{\alpha+1}+\frac{\beta-1}{\beta+1}$$ is

If $$\alpha, \beta$$ are the zeroes of $$a x^{2}+b x+c$$ then the value of $$\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$$ is

If $$\alpha, \beta$$ are the zeroes of $$a x^{2}+b x+c$$, then the value of $$\alpha^{5} \beta^{8}+\alpha^{8} \beta^{5}$$ is