<div class="table-container"><table><colgroup><col style="width: 200px;"><col style="width: 200px;"><col style="width: 200px;"></colgroup><thead><tr><th style="text-align: left; --cell-justify: flex-start"><p><strong>Discriminant</strong> \({{b}^{2}}-4ac&gt;0\)</p></th><th colspan="2" style="text-align: center; --cell-justify: center"><p>Shape of curve</p></th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start"><ul><li><p>\(a{{x}^{2}}+bx+c=0\) has two distinct real roots / two distinct real solutions.</p></li><li><p>The curve of \(y=a{{x}^{2}}+bx+c\) intersects the \(x\)-axis at two distinct points.</p></li></ul><p>&nbsp;</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div>
<div class="table-container"><table><colgroup><col style="width: 200px;"><col style="width: 200px;"><col style="width: 200px;"></colgroup><thead><tr style="height: 40px;"><th style="text-align: left; --cell-justify: flex-start"><p><strong>Discriminant</strong> \({{b}^{2}}-4ac=0\)</p></th><th colspan="2" style="text-align: center; --cell-justify: center"><p>Shape of curve</p></th></tr></thead><tbody><tr style="height: 43px;"><td style="text-align: left; --cell-justify: flex-start"><ul><li><p>\(a{{x}^{2}}+bx+c=0\) has two identical real roots / two identical real solutions.</p></li><li><p>The curve of \(y=a{{x}^{2}}+bx+c\) touches the \(x\)-axis at one point / the \(x\)-axis is a tangent to the curve.</p></li><li><p>The curve of \(y=a{{x}^{2}}+bx+c\) is such that \(y\) is always non-negative (\(a&gt;0\)), or, \(y\) is always non-positive (\(a&lt;0\)).</p></li></ul></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div>
<div class="table-container"><table><colgroup><col style="width: 200px;"><col style="width: 200px;"><col style="width: 200px;"></colgroup><thead><tr style="height: 40px;"><th style="text-align: left; --cell-justify: flex-start"><p><strong>Discriminant</strong> \({{b}^{2}}-4ac&lt;0\)</p></th><th colspan="2" style="text-align: center; --cell-justify: center"><p style="text-align: left;">Shape of curve</p></th></tr></thead><tbody><tr style="height: 43px;"><td style="text-align: left; --cell-justify: flex-start"><ul><li><p>\(a{{x}^{2}}+bx+c=0\) has no real root / no real solutions.</p></li><li><p>The curve of \(y=a{{x}^{2}}+bx+c\) does not intersect the \(x\)-axis.</p></li><li><p> The curve of \(y=a{{x}^{2}}+bx+c\) is such that \(y\) is always positive / above the \(x\)-axis (\(a&gt;0\)), or,&nbsp; \(y\) is always negative / below the \(x\)-axis (\(a&lt;0\)).</p></li></ul></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div>

<p style="text-align: left;">Shape of curve</p>

Nature of Roots of a Quadratic Equation in the Form of $a{{x}^{2}}+bx+c=0$

Nature of Roots of a Quadratic Equation in the Form of $a{{x}^{2}}+bx+c=0$