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8.
Find the zeroes of the quadratic polynomial P(x) = x2+x-12 and
verify the relationship between the zeroes and the coe

By Athena

8.
Find the zeroes of the quadratic polynomial P(x) = x2+x-12 and
verify the relationship between the zeroes and the coefficients.​

About the author
Athena

Describe how digital media with the use of electronic books affects the publishing
and printing industry​

T T
। प्रश्नचिन्हाच्या जागी योग्य संख्या निवडा.
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8
12

2 thoughts on “8.<br />Find the zeroes of the quadratic polynomial P(x) = x2+x-12 and<br />verify the relationship between the zeroes and the coe”

  1. Given Equation

    ⇒x² + x – 12 = 0

    To Find

    ⇒Zeroes of Quadratic Polynomial and

    ⇒verify the relationship between the zeroes and the coefficient

    Now take

    ⇒x² + x – 12 = 0

    Using Middle term Splitting

    ⇒x² + 4x – 3x – 12 = 0

    ⇒x(x + 4) – 3(x + 4) = 0

    ⇒(x – 3)(x + 4) = 0

    ⇒x – 3 = 0 and x + 4 = 0

    ⇒x = 3 and x = -4

    We Get

    ⇒α = 3 and β = -4

    Now verify relation

    ⇒Sum of root ( α + β ) = -b/a

    ⇒Product of root (αβ) = c/a

    Now Put the value on formula

    ( α + β ) = -b/a

    ⇒(3 – 4) = -1/1

    ⇒-1 = -1

    (αβ) = c/a

    ⇒(3×-4) = -12/1

    ⇒-12 = -12

    Hence Proved

    Reply

  2. ✰ Question Given :

    • Find the zeroes of the quadratic polynomial P(x) = x² + x – 12 and verify the relationship between the zeroes and the coefficients.

    ✰ Required Solution :

    ★ Equation given to us :

    • ➼ x² + x – 12

    ★ By Middle term Splitting :

    • ➼ x² + x – 12
    • ➼ x² + 4x – 3x – 12
    • ➼ (x² + 4x) – ( -3x – 12)
    • ➼ x ( x + 4 ) – 3 ( x – 4)

    ✰ Taking Common :

    • ➼ (x – 3 ) ( x + 4)

    ★ Comparing Both Sides :

    • ➼ ax + bx + c = 0

    ★ Values Calculated :

    • ➼ x = +3 ( Alpha) α
    • ➼ x = -4 (Beta) β

    ★ Verifying Relationship :

    • ➼ Sum of Zeros = ( α + β) = – b/a
    • ➼ Sum of Zeros = (- 4 + 3 ) = – 1
    • ➼ – 1 = – 1

    • ➼ Products of Zeros = ( α × β) = c / a
    • ➼ Products of Zero = ( – 4 × 3 ) = – 12

    • ➼ – 12 = – 12

    ⠀⠀⠀★ Hence Verified ! ★

    ______________________________

    Reply

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