Question

If p, q are the zeroes of the polynomial x2−5x+6, then p2+q2=​

Answer 1

Step-by-step explanation:

sum of zeroes= -b/a

= 5/1

p= 5

product of zeroes = c/a

= 6/1

q=6

p^2+q^2 = (5)^2+(6)^2

= 25+36

= 61

Answer 2

Required Answer:-

Given:

• p and q are the zeroes of the polynomial x² - 5x + 6.

To Find:

• The value of p² + q².

Solution:

Given,

→ x² - 5x + 6 = 0

Here,

• a = 1 (coefficient of x²)
• b = -5 (coefficient of x)
• c = 6 (constant term)

Relationship between zeroes and coefficient is given as :

• Sum of roots = -b/a
• Product of roots = c/a

Here, roots are p and q.

So,

→ p + q = -b/a

→ p + q = -(-5)/1

→ p + q = 5 – (i)

Also,

→ pq = c/a

→ pq = 6/1

→ pq = 6 – (ii)

So, the value of p² + q² will be,

= (p + q)² - 2pq

= 5² - 2 × 6

= 25 - 12

= 13

→ So, the value of p² + q² is 13.

Answer:

• p² + q² = 13.

Additional Info:

1. Quadratic formula:

→ ax² + bx + c = 0

→ x = (-b ± √(b² - 4ac))/(2a)

2. Discriminant of a quadratic equation:

→ D = b² - 4ac

Where,

• a = Coefficient of x².
• b = Coefficient of x.
• c = Constant term.

3. Nature of roots.

• If D > 0, roots are real and distinct.
• If D < 0, roots are imaginary.
• If D = 0, roots are real and equal.

4. Relationship between zeroes and coefficients.

• Sum of roots = -b/a
• Product of roots = c/a

5. A quadratic equation can have at most 2 zeroes.

•••♪