Question

If alpha and beta are the zeros of the polynomial f (x)=6x^2 + x-2 , then find the value of (i) alpha - beta

Answer 1

Given:

If alpha and beta are the zeros of the polynomial f(x)=6x^2 + x-2.

To find out:

Find the value of (i) α - β ?

Solution:

Since, α and β are the zeroes of the polynomial 6x² + x - 2.

• a = 6

• b = 1

• c = -2

Therefore,

★ Sum of zeroes:

α + β = -b/a

⇒ α + β = -1/6

★ Product of zeroes:

αβ = c/a

⇒ αβ = -2/6

⇒ αβ = -1/3

Now,

( α - β )² = ( α + β )² - 4αβ

( α - β )² = ( -1/6 )² - 4 × -1/3

( α - β )² = 1/36 + 4/3

( α - β )² = 1 + 48 / 36

( α - β )² = 49/36

α - β = √ 49/36

α - β = 7/6

Answer 2

ɢɪᴠᴇɴ :-

If α and β are the zeros of the polynomial f (x)=6x² + x-2 .

Tᴏ ғɪɴᴅ :-

• Value of (α - β)

sᴏʟᴜᴛɪᴏɴ :-

Now,

➦ f(x) = 6x² + x - 2

➭ On comparing the equation 6x² + x - 2 = 0 with ax² + bx + c = 0 , we get,

• a = 6
• b = 1
• c = -2

Now,

We know that,

➦ (α + β) = -b/a

➦ αβ = c/a

So,

➭ ( α + β) = -b/a = -1/6

➭ αβ = c/a = -2/6 = -1/3

Now,

We know that,

➦ ( α - β )² = (α + β)² - 4αβ

➭ (α - β)² = (-1/6)² - 4×-1/3

➭ (α - β)² = 1/36 + 4/3

➭ (α - β)² = 1/36 + 4×12/3×12

➭ (α - β)² = 1/36 + 48/36

➭ (α - β)² = 49/36

➭ (α - β) = √49/36

➭ (α - β) = 7/6

Hence,

• Value of (α - β) = 7/6