Quadratic Equations

In $$ax^2+bx+c=0$$ ,

$$\Delta=b^2-4ac$$

If $$Δ>0$$ , the quadratic equation has two equal real roots.

$$True\ or\ False$$

If α and β are the roots of the quadratic equation $$ax^2+bx+c=0\ is$$ .

$$\alpha+\beta=$$

Every quadratic equation has exactly two different real roots.

$$True\ or\ False$$

If the roots of the quadratic equation are $$α\ and\ β,$$ then the quadratic equation would be

$$x^2-(α+β)x+αβ=0$$

$$True\ or\ False$$

$$y=ax^2+bx+c$$ represents a parabola on the xy-plane, the roots of the equation will be the x-coordinate of the points where the parabola intersects the ............axis

$$y=ax^2+bx+c$$ represents a parabola on the xy-plane, the value of 'c' will be the y-coordinate of the point where the parabola intersects the ............axis

$$ax^2+bx+c=0$$

For the above quadratic, if one root is the reciprocal of the other, then $$c=a$$

If the roots of a quadratic equation are

(p + q) and (p − q), then the equation would be -

$$x^2−2px+(p^2−q^2)=0$$

$$True\ or\ False$$

The phrase 'the square of a number decreased by 5' can be mathematically written as $$5-x^2$$ .

$$True\ or\ False$$

The square of a girl's age is 20 more than 8 times her current age. The mathematical representation of this is -

$$x^2=8x+20$$

$$True\ or\ False$$