Class 10 Math Ex 1.2: Solved Notes & Practice MCQs
Master the Quadratic Formula with Teacher-Style Step-by-Step Solutions
Welcome to My Math Class!
Assalam-o-Alaikum Students! Today, we are going to learn something that will solve your math headaches forever. Remember in the previous exercise how we struggled to find factors? Sometimes the numbers were just too tricky to split. Well, that ends today because we are meeting the "Magic Formula" that solves any quadratic equation in seconds!
This "King of Formulas" is officially known as the Quadratic Formula. It never fails! All you need to do is bring your equation into the standard form ($ax^2 + bx + c = 0$), pick out the values of $a, b,$ and $c$, and feed them into this machine. The answer will pop right out!
In today's lesson, we won't just solve questions; we will learn how to stop being afraid of square roots and big numbers. I have broken down every question of Exercise 1.2 into simple steps so you feel like you're playing a game rather than studying. Grab your pens, and let’s start!
The Quadratic Formula:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Exercise 1.2 Solutions & Quiz
Q1: Solve 2 − x² = 7x
Step 1 (Standard Form): $x^2 + 7x - 2 = 0$
Step 2: $a=1, b=7, c=-2$
Step 3 (Calculation): $x = \frac{-7 \pm \sqrt{49 - 4(1)(-2)}}{2} = \frac{-7 \pm \sqrt{57}}{2}$
Checkpoint Quiz:
1.1: What is the constant term (c) here?
A) 2 | B) -2 | C) 7
Show Answer
B) -2
A) $x^2+7x-2=0$ | B) $x^2-7x+2=0$
Show Answer
A) $x^2+7x-2=0$
Q2: Solve 5x² + 8x + 1 = 0
Values: $a=5, b=8, c=1$
Formula: $x = \frac{-8 \pm \sqrt{64 - 20}}{10} = \frac{-8 \pm \sqrt{44}}{10}$
Simplify: $x = \frac{-4 \pm \sqrt{11}}{5}$
2.1: The value of $b^2-4ac$ is:
A) 44 | B) 84 Show Answer
A) 44
2.2: The denominator ($2a$) in this solution is:
A) 5 | B) 10 Show Answer
B) 10
Q3: Solve √3x² + x = 4√3
Values: $a=\sqrt{3}, b=1, c=-4\sqrt{3}$
Step: $b^2-4ac = 1 - 4(\sqrt{3})(-4\sqrt{3}) = 1 + 16(3) = 49$
Result: $x = \frac{-1 \pm 7}{2\sqrt{3}}$ gives $\sqrt{3}, \frac{-4}{\sqrt{3}}$
3.1: The square root of the discriminant ($\sqrt{49}$) is:
A) 7 | B) 9 Show Answer
A) 7
3.2: Multiplication of $\sqrt{3} \times \sqrt{3}$ is:
A) 9 | B) 3 Show Answer
B) 3
Q4: Solve 4x² − 14 = 3x
Standard Form: $4x^2 - 3x - 14 = 0$
Values: $a=4, b=-3, c=-14$
Calculation: $b^2-4ac = 9 - 4(4)(-14) = 233$
Result: $x = \frac{3 \pm \sqrt{233}}{8}$
4.1: Value of 'b' is:
A) 3 | B) -3 Show Answer
B) -3
4.2: This equation has how many roots?
A) 1 | B) 2 Show Answer
B) 2
Q5: Solve 6x² − 3 − 7x = 0
Standard Form: $6x^2 - 7x - 3 = 0$
Values: $a=6, b=-7, c=-3$
Discriminant: $b^2-4ac = 49 - 4(6)(-3) = 121$
Result: $x = \frac{7 \pm 11}{12} \rightarrow x = \frac{3}{2}, \frac{-1}{3}$
5.1: Square root of 121 is:
A) 11 | B) 12 Show Answer
A) 11
5.2: The sign of 'b' in the formula $-b$ becomes:
A) Positive | B) Negative Show Answer
A) Positive
💡 Teacher's Secret Tips
- Don't Rush: Always move all terms to one side to get a '0' on the right.
- Watch the Signs: If 'c' is negative, the $-4ac$ part will become positive. Be careful!
