Question

x^2-2x+5=0 check whether it is a quadratic equation steps expanation plz​

Answer 1

Yes.

Explanation :-

x²- 2x + 5 = 0

• Since, highest power is 1 .

• It is of the form ax² + bx + c = 0

• Where, a = 1 , b = -2 , c = 5

Hence, it is a quadratic equation.

Some Examples :-

Q. Find the discriminant of the equation: 3x² - 2x+⅓ = 0.

Solution:

Here, a = 3, b=-2 and c=⅓

Hence, discriminant, D = b² – 4ac

=> D = (-2)²-4 × 3× (⅓)

=> D = 4-4

=> D = 0 .

_______________

Q. Solve the equation x² + 4x-5=0, using completing the square method.

Solution:

x² + 4x – 5 = 0

=> x²+8/2x-5 = 0

=> x²+4/2x+4/2x-5 = 0

=> x²+2x+2x-5 = 0

=> (x + 2) x + 2 × x – 5= 0

=> (x + 2) x + 2 × x + 2 × 2 – 2 × 2 – 5= 0

=> (x + 2) x + (x + 2) × 2 – 2 × 2 – 5 = 0

=> (x+2) (x+2) -22 – 5 = 0

=> (x+2)² – 22 – 5 = 0

=> (x+2)² – 4 – 5 = 0

=> (x+2)² – 9 = 0

=> (x+2)² – 32 = 0

=> (x+2+3) (x+2-3) = 0 [By algebraic identities]

=> (x+5) (x-1) = 0

Therefore,

=> x = -5 & x = 1 .

Answer 2

Yes, the above is quadratic equation.

Solve with Quadratic Formula

Let's solve your equation step-by-step.

$\sf x^2-2x+5=0$

$\sf For \ this \ equation\ \rightarrow \\ a=1 \\b=-2 \\c=5$

Our equation now would be ⇒

$\sf 1x^2+-2x+5=0$

Step 1: Use quadratic formula with a = 1, b = -2, c = 5.

$\sf x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

$\sf x=\frac{-(-2)\± \sqrt{(-2)^2-4(1)(5)} }{2(1)}$

$\sf x=\frac{2\± \sqrt{-16} }{2}$

$\sf x = \frac{2 \± 4i}{2}$

∴ $\sf\bf x = \frac{2 \± 4i}{2}$ in the equation ⇒ $\sf\bf x^2-2x+5=0$.

Additional Information :)

What is a quadratic equation?

An equation which contains a variable and an exponent of 2 is known as a quadratic equation.

What is the quadratic formula?

The quadratic formula is ⇒ $\sf x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$