Question

what is quadratic equation?

Answer 1

$\huge\underline\mathrm{Question-}$

what is quadratic equation?

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Definition : A type of equation, having its degree ( highest power ) is 2.

General form : ax² + bx + c = 0

For finding the roots ( zeroes ) of this equation, we use quadratic formula. x can be said its zero.

$\huge{\red{\boxed{\mathrm{x=\dfrac{-b±\sqrt{D}}{2a}}}}}$

For applying it, we have find the value of D that is discriminant.

$\large{\boxed{\green{\mathrm{D=b^2-4ac}}}}$

★ When D = 0, roots are real and equal.

★ When D > 0, then roots are real and distinct.

★ When D < 0, then equation has no real roots.

We can also find the roots of quadratic equation by using splitting middle term or completing the square method.

Let $\alpha$ and $\beta$ are roots.

$\therefore$ sum of zeroes,

$\sf{\alpha+\beta=\dfrac{-b}{a}}$

$\therefore$ product of zeroes,

$\sf{\alpha×\beta=\dfrac{c}{a}}$

$\rule{200}2$

For example [ by using quadratic formula ], refer to the link given below :

https://brainly.in/question/15219749

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

• A quadratic equation in the variable x is an equation of the form $\bold {a{x}^{2} + bx + c = 0}$, where a,b,c are real numbers and $a \neq 0$.

• For example : $2 {x}^{2} + 3x + 1 = 0$.

• In other words, any equation of the form p (x) = 0, where p (x) is a polynomial of degree 2, is a quadratic equation.

• The standard form of the equation is $a {x}^{2} + bx + c = 0 , a \neq 0$.

• There are 2 zeroes of a quadratic equation.

• The parabola of a quadratic equation in variable x cuts the x-axis 2 times.

• The 3 ways to find the roots of a quadratic equation are :

1. Factorization method
2. Completing the square method
3. Quadratic formula or Shree Dhracharya formula

• In a factorization method, the x term or the middle term is splitted into two such that when we take out common, we get the roots.

• In completing the middle term method, leading term efficient has to be made 1. Then, the constant should be shifted to the right side and square of the half of the coefficient of x should be added to both the sides. Solving further, we get the roots.

• In quadratic equation, if ${b}^{2} - 4ac \geq 0$, the roots of the quadratic equation are given by : $\dfrac {-b \pm \sqrt{{b}^{2} - 4ac}}{2a}$.

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