Question

One of the zeroes of the polynomial 2x2 + 7x-4 is​

Answer 1

Two zeroes of 2x² + 7x - 4 is (1/2), and (-4)

Step by step explanation:

• The correct polynomial is P(x) = 2x² + 7x - 4

Now

By splitting middle term,

2x² + 8x - 1x - 4

⇒ 2x(x + 4) -1(x + 4)

[By taking 2x common in the first and second term, and taking (-1) common in third and fourth term]

⇒ (2x - 1)(x + 4)

So,

⇒ (2x - 1) = 0

⇒ 2x = 1

⇒ x = 1/2

And

⇒ (x + 4) = 0

⇒ x = (-4)

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• In a quadratic polynomial, there are two zeroes.
• In a cubic polynomial, there are three zeroes

Lets check whether (1/2) and (-4) are the zeroes of the polynomial P(x) = 2x² + 7x - 4 of not

P(1/2) = 2(1/2)² + 7(1/2) - 4

         = 2 * 1/4 + 7/2 - 4

         = 1/2 + 7/2 - 4

          = (1 + 7 - 8)/2

          = (8 - 8)/2

          = 0/2 = 0

And,

P(-4) = 2(-4)² + 7(-4) - 4

         = 2 * (16) - 28 - 4

         = 32 - 32

         = 0

Hence,

P(1/2), and P(-4) = 0, so

(1/2), and (-4) are the zeroes of the polynomial P(x) = 2x² + 7x - 4

Answer 2

Sᴏʟᴜᴛɪᴏɴ :-

Lᴇᴛ ᴘ (x) = 2x2 + 7x-4

= 2x2 + 8x-x-4 [ʙʏ sᴘʟɪᴛᴛɪɴɢ ᴍɪᴅᴅʟᴇ ᴛᴇʀᴍ]

= 2x(x+ 4)-1(x+ 4)

= (2x-1)(x+ 4)

Fᴏʀ ᴢᴇʀᴏᴇs ᴏғ ᴘ(x), ᴘᴜᴛ ᴘ(x) = 0 ⇒ (2x -1) (x + 4) =0

⇒ 2x-1 = 0 ᴀɴᴅ x+4 = 0

⇒ x = 1/2 ᴀɴᴅ x = -4

Hᴇɴᴄᴇ, ᴏɴᴇ ᴏғ ᴛʜᴇ ᴢᴇʀᴏᴇs ᴏғ ᴛʜᴇ ᴘᴏʟʏɴᴏᴍɪᴀʟ ᴘ(x) ɪs 1/2.