Verify that-i 4 is a zero of the polynomial px-x-4-ii -3 is a zero of the polynomial qx-x-3-iii 2 5is a zero of the polynomial- fx-2-5 x-iv -12 is a zero of the polynomial gy-2 y-1-

I #160;px=x 4 #8658;p4=4 4 nbsp; nbsp; nbsp; nbsp; nbsp; = 0 Hence, 4 is the zero of the given polynomial. ii #160;px= 3+3 #8658;p3=0 Hen ...

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Standard XII

Mathematics

Relations between Roots and Coefficients : Higher Order Equations

Verify that:i...

Question

Verify that:
(i) 4 is a zero of the polynomial p(x) = x − 4.
(ii) −3 is a zero of the polynomial q(x) = x + 3.
(iii) $\frac{2}{5}$ is a zero of the polynomial, f(x) = 2 − 5x.
(iv) $\frac{- 1}{2}$ is a zero of the polynomial g(y) = 2y + 1.

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Solution

$(i) p (x) = x - 4 \Rightarrow p (4) = 4 - 4$
= 0
Hence, 4 is the zero of the given polynomial.

$(ii) p (x) = (- 3) + 3 \Rightarrow p (3) = 0$
Hence, 3 is the zero of the given polynomial.

$(iii) p (x) = 2 - 5 x \Rightarrow p (\frac{2}{5}) = 2 - 5 \times (\frac{2}{5})$
$= 2 - 2 = 0$

Hence, $\frac{2}{5}$ is the zero of the given polynomial.

$(iv) p (y) = 2 y + 1 \Rightarrow p (- \frac{1}{2}) = 2 \times (- \frac{1}{2}) + 1 = - 1 + 1 = 0$

Hence, $- \frac{1}{2}$ is the zero of the given polynomial.

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Verify that: (i) 4 is a zero of the polynomial p(x) = x − 4. (ii) −3 is a zero of the polynomial q(x) = x + 3. (iii) 25is a zero of the polynomial, f(x) = 2 − 5x. (iv) -12is a zero of the polynomial g(y) = 2y + 1.

i px=x-4⇒p4=4-4 = 0 Hence, 4 is the zero of the given polynomial. ii px=-3+3⇒p3=0 Hence, 3 is the zero of the given polynomial. iii px=2-5x⇒p25=2-5×25 =2-2=0 Hence, 25 is the zero of the given polynomial. iv py=2y+1⇒p-12=2×-12+1 =-1+1 =0 Hence, -12 is the zero of the given polynomial.

Verify that:
(i) 4 is a zero of the polynomial p(x) = x − 4.
(ii) −3 is a zero of the polynomial q(x) = x + 3.
(iii) $\frac{2}{5}$ is a zero of the polynomial, f(x) = 2 − 5x.
(iv) $\frac{- 1}{2}$ is a zero of the polynomial g(y) = 2y + 1.