✔ Sum formula is -b/a. Here b=3, a=2. So result is -3/2.
Q2. What is the product of zeros for x^2 - 4?
✔ Product is c/a. Here c=-4, a=1. So result is -4/1 = -4.
Q3. If sum is 5 and product is 6, which polynomial matches?
✔ Equation is x^2 - (sum)x + product = 0. So x^2 - 5x + 6.
Show transcript
[Slide 1] Understanding Polynomial Roots
Welcome students. Today we link roots to coefficients. This helps solve questions quickly without finding roots first.
[Slide 2] The Key Formulas
For any quadratic, sum is negative b by a. Product is simply c by a. Memorize these two relations for exams.
[Slide 3] Worked Example Setup
Let us take a concrete example. Here a is one, b is negative five. We will verify the relationship using actual roots.
[Slide 4] Verifying the Relationship
The roots are two and three. Their sum is five, matching negative b by a. Product matches c by a perfectly.
[Slide 5] Common Student Mistake
Many students forget the negative sign in sum. Do not write b by a for sum. Always check the sign carefully.
[Slide 6] Quick Recap
Remember sum is negative b by a. Product is c by a. Practice these to score full marks.