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Q.

If the Discriminant is zero for a Quadratic Equation, then


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a

 Graph will intersect the x-axis at two points.

b

 The graph will touch the x-axis.

c

 The graph will be above the x-axis.

d

 None of the above.

answer is B.

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Detailed Solution

Concept:
The value of the discriminant can be used to determine the nature of the quadratic equation’s roots. The points where the curve meets the x-axis are the roots of an equation. As a result, we can determine the nature of the root to predict the graph.
As we know that,
Discriminant describes the nature of the roots where https://lh3.googleusercontent.com/SXjVC-mLpfhC53P4HOT0POTZWubSILsoP-ypYvtUuepSq2PwrAYY2g0YU17fXiHk217KFwGDf8c-jT9bosXIabPb_5t_ZkMc9yZC-XcnGbiyWM9OZZfsxPqHng8WPTGkIHfDb3Ilr7W2gkq-VK6BqACase 1:
If https://lh4.googleusercontent.com/Cayn0ObXsxMCcOlAtnAoIaaddRCAbCrJXP1l0KhAknne_UPawt8-4rEoMsJCdOTlq8pglr-_6ziUTfdoXHlMLTKPnEde0hYFlbGGlYn64DSywiefVIID5A44U21QTYE5CqJhoWqqvGGpeZyjPcq2Ng, equation has https://lh6.googleusercontent.com/-ay1BWjP6lpIRBLstCCy1osXuHYsWKOiX_d3LJQ1t6ZBGbKKE4CqRWxr5PHYpN5wii077mxs61WTvWYg_InRcDUBuxlRFxlwUBfq4fqadkEJLC5fBSQvle-Ld3xbTLRNQS8BK3n8gywtxNWCt9WZeg real and distinct roots. Therefore, the curve will meet the x-axis at two points.
seoCase 2:
If https://lh3.googleusercontent.com/edfdTFoHoXhvdVZ_f1kMtD1sgHWRfI_7jukdyRCVFHNs2Vleu80Q_a5zXl99F3gUmXxk92fth5pmCEZkkbCUQrBKeKDLvo-BIMi573GwPG84XXnghB9mtOukm9K1Y4tRarzHvmwMK0u1eBg-UVHKwQ, equation has https://lh5.googleusercontent.com/4Gna_SLtORFDVhQlynSs2CN53yw_MSx9T4LfO52jW6emlcL2p2ulI7jgrkeIKfqUI14tP-oueL7uRmWE0qEn75Ba5IO4O-AtMMfUit5yc8MOhKAEKiLluc5470EYxL6n1LLyHMO9zwt_ltf2BvOwiQ real root. Therefore, the curve will meet the x-axis at only one point.
seoCase 3:
If https://lh3.googleusercontent.com/f84BiWc00RjNEBt35dPIP7eEfxi-cGN1xKgxhke-QQ82BBZ6h5O4bORzlHZVRQA9wxTxcXL8cQIQmo42vFq2IzlyVfa859bi_tM2WhRWqqvDuS6_J8pbGWtc4Qf0QPUuE6ScTKLdBO2ZeN6_kILARg, equation has no real roots. Therefore, the curve doesn’t meet the x-axisseoHence, the correct answer is option 2) The graph will touch the x-axis
 
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