Quadratic Equations: CBSE Class 10 Mathematics practice questions

C. $a\ne 0$

The equation is quadratic because of the $ax^2$ term. If $a=0$ that term vanishes and only $bx+c=0$ is left, a linear equation (the picture's curve flattens to a line). $b$ or $c$ can be zero: $2x^2-8=0$ ($b=0$) and $3x^2+5x=0$ ($c=0$) are both quadratic, so the other conditions are not needed.

B. $(x+3)^3=x^3-9$

$(x+3)^3=x^3+9x^2+27x+27$, so $(x+3)^3=x^3-9$ becomes $9x^2+27x+36=0$: it looks cubic but is quadratic. In the others the $x^2$ (or $x^3$) terms cancel: $x^2+4x+7=x^2-9$ gives $4x+16=0$; $x^2-4x+4=x^2+5x$ gives $-9x+4=0$; $x^3+x=x^3+2x+3$ gives $-x-3=0$. All three are linear.

A. 40 km/h

Let the speed be $x$ km/h. Then $\dfrac{480}{x-8}-\dfrac{480}{x}=3$, which simplifies to $x^2-8x-1280=0$, i.e. $(x-40)(x+32)=0$. The speed cannot be negative, so $x=40$ km/h (times: 12 h and 15 h, a difference of 3 h). 32 is the reduced speed, 48 is $x+8$, and 160 is $480\div3$, which ignores the equation.