relationship between zeroes and coefficients : u^2-5u
Answers
Answer- The above question is from the chapter 'Polynomials'.
Let's know about quadratic polynomial first.
Quadratic polynomial- A polynomial whose highest power of variable is 2 is called a quadratic polynomial.
Examples:
1) x² + 2x + 2
2) 2x² + 4x + 1
Relationship between zeroes and coefficients of a quadratic polynomial:
Let p(x)= ax² + bx + c be any quadratic polynomial in x.
Let α and β be its zeroes.
Sum of zeroes i.e α and β= -b/a
Product of zeroes i.e αβ= c/a
Question: Verify relationship between zeroes and coefficients: u² - 5u.
Solution: Let p(x) = u² - 5u
= u (u - 5) (Taking u as common)
Let p(x) = 0
u (u - 5) = 0
Either u = 0
OR u - 5 = 0
⇒u = 5
∴ Zeroes of p(x) = u² - 5u = 0 and 5.
Here, a = 1, b = -5 and c = 0.
Verification:
Sum of zeroes = 0 + 5 = 5
Sum of zeroes = -b/a = -(-5)/1 = 5
So, sum of zeroes = -b/a
Product of zeroes = 0 × 5 = 0
Product of zeroes = c/a = 0/1 = 0
So, product of zeroes = c/a
Hence, verified.