Key Concepts
- 1Sum of zeroes (quadratic)
- 2Product of zeroes (quadratic)
- 3Polynomial from zeroes
- 4Number of zeroes from graph
- 5Degree of a polynomial
- 6α² + β² in terms of sum/product
- 71/α + 1/β in terms of sum/product
- 8Sum of zeroes (quadratic)
- 9Product of zeroes (quadratic)
- 10Polynomial from zeroes
Important Formulas & Facts
#1
For ax² + bx + c: α + β = -b/a
#2
For ax² + bx + c: αβ = c/a
#3
p(x) = x² - (sum)x + (product)
#4
Count the number of points where the graph crosses the x-axis.
#5
Highest power of the variable. Linear: 1, Quadratic: 2, Cubic: 3
#6
α² + β² = (α + β)² - 2αβ
#7
1/α + 1/β = (α + β)/(αβ)
#8
For ax² + bx + c: α + β = -b/a
#9
For ax² + bx + c: αβ = c/a
#10
p(x) = x² - (sum)x + (product)
Must-Know Questions
Q1Find the zeroes of the polynomial x² - 3.
Explanation
x² - 3 = 0 → x² = 3 → x = ±√3.
Q2If α and β are zeroes of x² - 5x + 6, find α + β and αβ.
Explanation
For ax² + bx + c: sum = -b/a = 5, product = c/a = 6.
Q3Find a quadratic polynomial whose zeroes are 2 and -3.
Explanation
Sum = 2 + (-3) = -1. Product = 2 × (-3) = -6. Polynomial: x² - (sum)x + product = x² + x - 6.
Q4If one zero of 2x² - 3x + k is reciprocal of the other, find k.
Explanation
Let zeroes be α and 1/α. Product = c/a = k/2. Also α × (1/α) = 1. So k/2 = 1, k = 2.
Q5The number of zeroes of y = p(x) is the number of points where the graph intersects the:
Explanation
The zeroes are the x-coordinates where the graph crosses the x-axis.
Practice Polynomials
Reinforce what you just revised with practice questions