Quadratic Roots Formulas

Very Important

The General Quadratic equation will be in the form of a$$x^{2}$$+b$$x$$+c = 0

The values of ‘x’ satisfying the equation are called the roots of the equation.

The value of roots, p and q = $$\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$

The sum of the roots = p+q = $$\dfrac{-b}{a}$$

Product of roots = p*q = $$\dfrac{c}{a}$$

If c and a are equal then the roots are reciprocal to each other.

If b = 0, then the roots are equal and are opposite in sign.

If roots are given : (x-a)(x-b)=0 => $$x^2 - (a+b)x + ab = 0$$

If sum s and product p of roots are given: $$x^2 - sx + p = 0$$


    Formula Video


    Question 1

    Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

    Question 2

    Suppose one of the roots of the equation $$ax^{2}-bx+c=0$$ is $$2+\sqrt{3}$$, Where a,b and c are rational numbers and $$a\neq0$$. If $$b=c^{3}$$ then $$\mid a\mid$$ equals.

    Question 3

    Consider the pair of equations: $$x^{2}-xy-x=22$$ and $$y^{2}-xy+y=34$$. If $$x>y$$, then $$x-y$$ equals

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