Question

write the nature of roots from the given values of the discriminants and complete the activity.

Answer 1

hey mate
we compare nature root by discriminant
lets take d as discriminant =b^2-4ac
so we d>0 real roots
d<0 imaginary roots
d=0 equal roots
so fr ur ques
answers are
1 ,real roots
2,img roots
3,equal roots
4,real roots
i hope u understood!!

Answer 2

Answer:

$\begin{array}{|c|c|}\cline{1-2}{\sf\:Value\:of\:the\:discriminant & \sf\:Nature\:of\:roots}\\\cline{1-2}{25\:\:\:\longrightarrow & \sf\:Real\:\&\:unequal}\\\cline{1-2}{-\:23\:\:\:\longrightarrow & \sf\:Not\:real}\\\cline{1-2}{0\:\:\:\longrightarrow & \sf\:Real\:\&\:equal}\\\cline{1-2}{10\:\:\:\longrightarrow & \sf\:Real\:\&\:unequal}\\\cline{1-2}\end{array}$

Step-by-step-explanation:

The value of discriminant is calculated by

$\sf\:b^2\:-\:4ac$.

Here, we have given the values of discriminant.

We have to find the nature of roots of the quadratic equation.

The nature of roots is found.

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula to solve quadratic equation:

$\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}$

5. Value of Δ and nature of roots:

$\begin{array}{|c|c|}\cline{1-2}{\triangle = 0 & \sf\:Real\:and\:equal}\\\cline{1-2}{\triangle > 0 & \sf\:Real\:and\:unequal}\\\cline{1-2}{\triangle < 0 & \sf\:Not\:real}\\\cline{1-2}\end{array}$