Question

If one of the zeroes quadratic polynomial p(x) = 2x^2 − (k+ 5)x + 6 is 3. Find the other zero, also find the value k.​

Answer 1

Given:-

• p(x) = 2x² - ( k + 5 ) x + 6
• One zero → 3

To find :—

• The other zero .
• The value of k .

Now,

p(x) = 2x² - ( k + 5 ) x + 6

† 3 is one of the zeros of the polynomial .

So, p(3) = 0

→ 2×3² - (k+5)3 + 6 = 0

→ 2 × 9 - ( k+5)3 + 6 = 0

→ 18 - 3k - 15 + 6 = 0

→ 3k = 18 + 6 - 15

→ 3k = 24 - 15

→ 3k = 9

→ k = 9/3

→ $\underline{\bold{\color{blue}{k\:\:=\: 3}}}$

So, the value of k → 3 .

Now, the quadratic polynomial,

★ p(x) = 2x² - ( 3 + 5 )x + 6

→ p(x) = 2x² - 8x + 6 .

• Now we have to find the other zero .

So, p(x) will be ‘0' when ,

† 2x² - 8x + 6 = 0

→ 2x² - 2x - 6x + 6 = 0

→ 2x (x - 1) - 6 ( x - 1 ) = 0

→ ( 2x - 6 ) ( x -1 ) = 0

→ 2x - 6 = 0

or x - 1 = 0

→ 2x = 6

or x = 1

→ x = 3

or x = 1

★ So the other zero is ☞ 1