SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Quadratic Equations

13 questions · 13 still being checked

EXERCISE 4.3 1–5 (part 3 of 3)

  1. Exercise 1

    Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
    (i)
    2x2−3x+5=0\displaystyle 2 x^{2}-3 x+5=0
    (ii)
    3x2−43x+4=0\displaystyle 3 x^{2}-4 \sqrt{3} x+4=0
    (iii)
    2x2−6x+3=0\displaystyle 2 x^{2}-6 x+3=0
    NCERT’s answer
    (i)
    Real roots do not exist (ii) Equal roots; $\displaystyle \frac{2}{\sqrt{3}}, \frac{2}{\sqrt{3}}$ (iii) Distinct roots; $\displaystyle \frac{3 \pm \sqrt{3}}{2}$

    Working being prepared

  2. Exercise 2

    Find the values of k\displaystyle k for each of the following quadratic equations, so that they have two equal roots.
    (i)
    2x2+kx+3=0\displaystyle 2 x^{2}+k x+3=0
    (ii)
    kx(x−2)+6=0\displaystyle k x(x-2)+6=0
    NCERT’s answer
    (i)
    $\displaystyle k= \pm 2 \sqrt{6}$ (ii) $\displaystyle k=6$

    Working being prepared

  3. Exercise 3

    Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2\displaystyle 800 \mathrm{~m}^{2} ? If so, find its length and breadth.
    NCERT’s answer
    Yes. $\displaystyle 40$ m, $\displaystyle 20$ m

    Working being prepared

  4. Exercise 4

    Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20\displaystyle 20 years. Four years ago, the product of their ages in years was 48.
    NCERT’s answer
    No

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  5. Exercise 5

    Is it possible to design a rectangular park of perimeter 80\displaystyle 80 m and area 400 m2\displaystyle 400 \mathrm{~m}^{2} ? If so, find its length and breadth.
    NCERT’s answer
    Yes. $\displaystyle 20$ m, $\displaystyle 20$ m

    Working being prepared