Question

LEVEL-1
1. Find the zeros of each of the following quadratic polynomials and verify the
relationship between the zeros and their coefficients:
(v) p(x) = x2 + 2 root 2 x - 6


Hope this would help…
Btw this is an RD question on pg. no. 2.33

Answer 1

The polynomial given is :

• x² + 2√2x - 6

Factorising the polynomial by splitting the middle term :

• x² + 2√2x - 6
• x² + 3√2x - √2x - 6
• x (x + 3√2) - √2 (x + 3√2)
• (x + 3√2) (x - √2)

Finding the zeroes :

★ (x + 3√2) :

• x + 3√2 = 0
• x = - 3√2

★ (x - √2)

• x - √2 = 0
• x = √2

Let the zeroes be :

• α = - 3√2
• β = √2

Finding the sum and product of the zeroes :

★ Sum of the zeroes :

• - 3√2 + √2
• - 2√2 = α + β

★ Product of the zeroes :

• - 3√2 (√2)
• - 3 (2)
• - 6 = αβ

When we compare the polynomial x² + 2√2x - 6 to ax² + bx + c, we get the values as :

• a = 1
• b = 2√2
• c = - 6

Verifying the relationship between the zeroes and the coefficients :

★ Sum of zeroes :

• α + β = - b/a
• - 2√2 = - 2√2/1
• - 2√2 = - 2√2
• LHS = RHS

★ Product of zeroes :

• αβ = c/a
• - 6 = - 6/1
• - 6 = - 6
• LHS = RHS

H E N C E , V E R I F I E D !

S U M - P R O D U C T P A T T E R N :

In the polynomial x² + 2√2x - 6 :

★ Product :

• - 6 × x²
• - 6x²

★ Sum :

• 3√2x - √2x
• 2√2x

★ Sum and product :

• 3√2 (-√2)
• 3 (-2)
• - 6

★ In the polynomial :

• 3√2x (-√2x)
• 3 (-2x²)
• - 6x²
• Got it!