Question

if alpha and beta are the zeros of the quadratic polynomial p(x) = x² -8x +12 then find the value of alpha / beta + beta by alpha ..... guys please asap I hv my exam within few min ... Class X

Answer 1

Answer:

just follow this steps and replace the numbers it is same

Answer 2

Gɪᴠᴇɴ :-

• ɑ and β are the zeros of the quadratic polynomial p(x) = x² -8x + 12.

Tᴏ Fɪɴᴅ :-

• (ɑ/β) + (β/ɑ)

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)
• Product of roots of the Equation is given by = c/a.
• (a² + b²) = (a + b)² - 2ab

Sᴏʟᴜᴛɪᴏɴ :-

comparing the given Quadratic Equation p(x) = x² -8x +12 = 0 with ax² + bx + c = 0 we get,

→ a = 1

→ b = (-8)

→ c = 12

so,

→ ɑ + β = (-b/a) = -(-8)/1 = 8

→ ɑ * β = c/a = 12/1 = 12

Now,

→ (ɑ/β) + (β/ɑ)

Taking LCM ,

→ (ɑ² + β²) / (ɑ*β)

using formula (a² + b²) = (a + b)² - 2ab in Numerator now,

→ {(ɑ + β)² - 2ɑ*β} / (ɑ*β)

Putting values Now, we get,

→ {(8)² - 2*12} / 12

→ (64 - 24)/12

→ 40/12

→ 10/3 (Ans.)