Question

1 Check whether 1, -1 and¼ are zeroes of the polynomial p(x) = 4x + 3x - 1.​

Answer 1

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⇝ ZEROES OF POLYNOMIAL :

• Let p(x) be a polynomial. If p(α) = 0 then we say that α is a zero of the polynomial p(x).

⇝ REMARK :

• Finding the zeroes of a polynomial p(x) means solving the equation p(x) = 0

⇝ REQUIRED SOLUTION :

Given, p(x) = 4x + 3x - 1

• Putting, p(1) = 4 × 1 + 3 × 1 - 1

= 4 + 3 - 1

= 7 - 1

= 6 ≠ 0

• Putting, p(-1) = 4 × (-1) + 3 × (-1) - 1

= - 4 - 3 - 1

= - 7 - 1

= - 8 ≠ 0

• Putting, p(¼) = 4 × ¼ + 3 × ¼ - 1

= ⁴/₄ + ¾ - 1

= (4 + 3 - 4)/4

= (7 - 4)/4

= ¾ ≠ 0

∴ 1, -1 & ¼ is not the zero of the p(x).

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