Draw the graph of each of the following equations:
(i) x = 5
(ii) y = −2
(iii) x + 6 = 0
(iv) x + 7 = 0
(v) y = 0
(vi) x = 0

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Solution

(i) x = 5
(ii) y = -2
(iii) x + 6 = 0 ⇒ x = -6
(iv) x + 7 = 0 ⇒ x = -7
(v) y = 0
(vi) x = 0

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Find the nature of the roots of the following quadratic equations:
(i) $2 x^{2} - 8 x + 5 = 0$

(ii) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$
(iii) $5 x^{2} - 4 x + 1 = 0$

(iv) $5 x (x - 2) + 6 = 0$
(v) $12 x^{2} - 4 \sqrt{15} x + 5 = 0$

(vi) $x^{2} - x + 2 = 0$

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