Question

what do you think is the significance of knowing the sum and the product of the roots of quadratic equations ​

Answer 1

Answer:

Step-by-step explanation:

The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient. The product of the roots of a quadratic equation is equal to the constant term (the third term), ... The roots will be represented as r1 and r2.

Answer 2

The significance of the sum and the product of the roots of a quadratic equation can be found from their definition and formula.

Suppose, we have a quadratic equation,

$ax^2+bx+c=0$

Let the roots of the above equation be $r_1$ and $r_2$

The roots of the quadratic equation can be represented by the Sridhar-Acharya Rule which is,

$r_1=\frac{-b+\sqrt{b^2-4ac} }{2a}$

$r_2 = \frac{-b-\sqrt{b^2-4ac} }{2a}$

The sum of the roots is,

$r_1+r_2 = \frac{-b+\sqrt{b^2-4ac}-b-\sqrt{b^2-4ac} }{2a}$

⇒ $-\frac{2b}{2a}=\frac{b}{a}$

The product of roots is,

$r_1*r_2=(\frac{-b-\sqrt{b^2-4ac} }{2a})*(\frac{-b+\sqrt{b^2-4ac} }{2a})$

$=\frac{b^2-b^2+4ac}{4a^2}=\frac{c}{a}$

As we can see that the sum of the roots is the negative value of the coefficient of $x$ divided by the constant while the product of the roots will be equal to the constant divided by the coefficient of $x^2$