Quadratic Equations

If the graph of a quadratic polynomial $$ax^2+bx+c$$ does not touch or cut the X-axis (as shown above), which of the following statements is correct?

Find the roots of the following quadratic equations,if they exist,using the quadratic formula of shridhar Acharya.
$$9x^2+7x-2=0$$
If the curve $$y = c_1e^{m_1x} + c_2e^{m3x}$$, where $$c_1, c_2, c_3$$ are arbitrary constants and $$m_1, m_2, m_3$$ are roots of $$m^3 - 7m + 6 = 0$$
If $$x = \dfrac{{\sqrt {2a + 1}  + \sqrt {2a - 1} }}{{\sqrt {2a + 1}  - \sqrt {2a - 1} }}$$, then show that $${x^2} - 4ax + 1 = 0$$
Compare the given quadratic equations to the general form and write values of $$a, b, c$$.
$$2m^{2} = 5m - 5$$