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# Tips And Tricks And Shortcuts For Quadratic Equations

**Tips and Tricks and Shortcuts for ****Quadratic Equation**

Quadratic Equation is an equation which is written in the standard form is ax² + bx + c = 0 with a, b, and c being constants and x is an variable. That’s why it is also known as second degree equation . Here, we will be discussing about tips and tricks for quadratic equations.

- On, solving the quadratic equations generally we get two linear equations.
- Here, are some quick shortcuts and easy tips and tricks for you to solve Quadratic Equation questions quickly, easily, and efficiently in various competitive exams and recruitment exams.
- There are generally two in of Quadratic Equations.

- Factorization
- Completing the square method.
- Quadratic Formula

### Tips and shortcuts to solve the Quadratic Equation questions

- In order to find the sign of roots we use sign given in the equation.

Sign of coefficient ‘x’ | Sign of coefficient ‘y’ | Sign of roots |

+ | + | – – |

+ | – | – + |

– | + | + + |

– | – | + – |

For example: x^{2} + 3x – 4 = 0

The factors are 4 and 1

Now will find the sign of roots. According to the table, if sign given in the equation is + and – then their sign of roots is – and +.

Therefore, the roots of the equation are -4 and 1

### Type 1: Tricks and Shortcuts for Quadratic Questions

- When one equation has positive roots and other has negative, or equations has same sign roots, then compare the roots and find the relation between them.

**Question 1. Find the correct option given below by solving the following equation ****x ^{2} – 7x + 10 = 0 and **

**y**

^{2}+ 8y + 15 = 0**Options:**

**A. x < y****B. x > y****C. x ≤ y****D. x ≥ y****E. cannot be determined**

**Solution:** x^{2} – 7x + 10 = 0…. (1)

Roots of first equation are 5 and 2

Using the table above, we will find the sign of roots. If sign given in the equation is – and + then their sign of roots is + and +

Therefore, the roots of the equation are 5 and 2

Now, y^{2} + 8y + 15 = 0 ……. (2)

Roots of second equation are 3 and 5

If sign given in the equation is + and + then their sign of roots is – and –

Therefore, the roots of the equation are -3 and – 2

Now, here roots are +x1, + x2, – y1, and – y2

This clearly shows that X roots are positive and Y roots are negative. So, x> y

**Correct option: B**

### Type 2: Tips and Tricks To Solve Quadratic Equations Questions

- When roots of the equation are positive and negative and we cannot find the relation between them.

**Question 1 Find the correct option given below by solving the following equation **6x^{2} + 11x – 35 = 0 and 6y^{2} + 5y – 6 = 0

**Options:**

**A. x < y****B. x > y****C. x ≤ y****D. x ≥ y****E. cannot be determined**

**Solution: **6x^{2} + 11x – 35 = 0…. (1)

Roots of first equation are 3.5 and 1.66

Using the table above, we will find the sign of roots. If sign given in the equation is + and – then their sign of roots is – and +

Therefore, the roots of the equation are – 3.5 and 1.66

Now, 6y^{2} + 5y – 6 = 0 ……. (2)

Roots of second equation are 1.5 and 0.66

If sign given in the equation is + and – then their sign of roots is – and +

Therefore, the roots of the equation are – 1.5 and 0.66

Now, here roots are -x_{1}, + x_{2}, – y_{1}, and + y_{2}

It means x_{2}> – y_{1} and –x_{1}< + y_{2}

So, we cannot determine which roots are greater.

**Correct option: E**

### Type 3: Tips and Tricks and Shortcuts for Quadratic Questions

- When we can find a equation where x is a variable and a, b, and c represent constants and D, i.e., Discriminant.
- The discriminant is the part of the quadratic formula
**underneath the square root symbol: b²-4ac**.3x

Question 1 Find the Discriminant and roots of the following equation^{2 }− 5x − 7 = 0Let us find Discriminant, D = \sqrt{B^{2}-4AC}

D = \sqrt{(-5)^{2}-4(3)(-7)}

D = 109

Therefore, x = \frac{-b \pm \sqrt{}D}{2a}

x = \frac{5 \pm \sqrt{}109}{6}

x = \frac{5 \pm 10.44}{6}

x = \frac{15.44}{6} => x = 2.57 , and

x = \frac{-5.44}{6} => x = – 0.90

So the two roots are 2.57 and -0.90

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- Linear Equations – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Quadratic Equations – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

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